Deck 9: Inverse Functions

Question 1

Select the correct graph,showing f and g are inverse functions.? $$f ( x ) = \sqrt { x - 3 } , g ( x ) = x ^ { 2 } + 3 , x \geq 0$$ ?

A)
B)
C)
D)
E)

Answer 1

Question 2

Determine whether the function has an inverse function.If it does,find the inverse function. ?
G(x)= x⁷
?

A) $g ^ { - 1 } ( x ) = \frac { 7 } { x }$
B)g^-1(x)= -7x
C)? $$g ^ { - 1 } ( x ) = - \frac { x } { 7 }$$
D)g^-1(x)= 7x
E)The inverse exists,but none of the above

Answer 2

The inverse exists,but none of the above

Question 3

Find the inverse function of $f ( x ) = \sqrt { 36 - x ^ { 2 } } , 0 \leq x \leq 6$ . ?

A) $f ^ { - 1 } ( x ) = \sqrt { 36 - x ^ { 2 } } , 0 \leq x \leq 6$
B) $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } - 36 } , 0 \leq x \leq 6$
C) $f ^ { - 1 } ( x ) = 36 - x ^ { 2 } , 0 \leq x \leq 6$
D) $f ^ { - 1 } ( x ) = \sqrt { 36 + x ^ { 2 } } , 0 \leq x \leq 6$
E) $f ^ { - 1 } ( x ) = 36 + x ^ { 2 } , 0 \leq x \leq 6$

Answer 3

$f ^ { - 1 } ( x ) = \sqrt { 36 - x ^ { 2 } } , 0 \leq x \leq 6$

Question 4

Select the graph of f and f^-1 on the same set of coordinate axes.? $$f ( x ) = \frac { 3 } { x }$$ ?

A) ?
B)
C)?
D)?
E)

Question 5

Select the correct graph,showing f and g are inverse functions.? $$f ( x ) = 9 x , g ( x ) = \frac { x } { 9 }$$ ?

A)
B)
C)
D)
E)

Question 6

Select the graph of the function,and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function.? $$g ( x ) = \frac { 4 - x } { 5 }$$ ? ?

A) The function has an inverse.
B)? The function has an inverse.
C)? The function has an inverse.
D)? The function has an inverse.
E)? The function has an inverse.

Question 7

Does the function have an inverse function?​ ​

A)No
B)Yes

Question 8

Select the graph of the function,and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function.? $$g ( x ) = - 2 x \sqrt { 6 - x ^ { 2 } }$$ ? ?

A)? The function does not have inverse.
B)? The function does not have inverse.
C)? The function does not have inverse.
D)? The function does not have inverse.
E)? The function does not have inverse.

Question 9

Select the graph of the function,and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. ​
G(x)= |x + 5| - |x - 5|
​

A)​ The function does not have inverse.
B)​ The function does not have inverse.
C)​ The function does not have inverse.
D)​ The function does not have inverse.
E) The function does not have inverse.

Question 10

Select the correct graph,showing f and g are inverse functions.? $$f ( x ) = 6 - x ^ { 2 } , g ( x ) = \sqrt { 6 - x } , x \leq 6$$ ?

A)
B)
C)
D)
E)

Question 11

Select the correct graph,showing f and g are inverse functions.? $$f ( x ) = \frac { x - 1 } { x + 8 } , g ( x ) = - \frac { 8 x + 1 } { x - 1 }$$ ?

A)?
B)?
C)
D)
E)

Question 12

Does the function have an inverse function?​ ​

A)No
B)Yes

Question 13

Select the correct graph,showing f and g are inverse functions.? $$f ( x ) = 6 x + 1 , g ( x ) = \frac { x - 1 } { 6 }$$ ?

A)
B)
C)
D)
E)

Question 14

Find the inverse function of f informally. ?
F(x)= x⁴
?

A) $f ^ { - 1 } ( x ) = 4 \sqrt { x }$ ?
B) $f ^ { - 1 } ( x ) = \sqrt [ 4 ] { x }$
C) $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt [ 4 ] { x } }$
D) $f ^ { - 1 } ( x ) = ( \sqrt [ 4 ] { x } ) ^ { 4 }$
E) $f ^ { - 1 } ( x ) = - \sqrt [ 4 ] { x }$

Question 15

Select the graph of f and f^-1 on the same set of coordinate axes. ​
F(x)= 2x - 3
​

A)
B)
C)
D)
E)​

Question 16

Select the correct graph,showing f and g are inverse functions.? $$f ( x ) = \frac { x ^ { 3 } } { 7 } , g ( x ) = \sqrt [ 3 ] { 7 x }$$ ?

A)
B)
C)
D)
E)

Question 17

Find the inverse function of g(x)= x² - 3 informally. ?

A) $g ^ { - 1 } ( x ) = \sqrt [ 2 ] { x - 3 }$
B) $g ^ { - 1 } ( x ) = ( x + 3 ) ^ { 2 }$
C) $$g ^ { - 1 } ( x ) = x ^ { 2 } + 3$$
D) $g ^ { - 1 } ( x ) = \sqrt [ 2 ] { x + 3 }$
E) $$g ^ { - 1 } ( x ) = ( x - 3 ) ^ { 2 }$$

Question 18

Find the inverse function of f informally. ?
F(x)= 6x
?

A)f^-1(x)= 6 - x
B)f^-1(x)= 6 + x
C) $f ^ { - 1 } ( x ) = \frac { 1 } { 6 } x$
D)f^-1(x)= x - 6
E)f(x)= 6x

Question 19

Find the inverse function of f informally. ?
F(x)= x - 5
?

A)f^-1(x)= - (x + 5)
B)? $f ^ { - 1 } ( x ) = \frac { 5 } { x }$
C) $f ^ { - 1 } ( x ) = \frac { x } { 5 }$
D)f^-1(x)= 5 - x
E)f^-1(x)= x + 5

Question 20

Use the tables of values for y = f(x)to complete a table for y = f ^-1(x).
$$\begin{array} { | r | l | l | l | l | l | l | } \hline x & - 3 & - 2 & 0 & 1 & 2 & 3 \\\hline f ( x ) & - 4 & - 2 & 2 & 4 & 6 & 8 \\\hline\end{array}$$

A) $$\begin{array} { | l | l | l | l | l | l | l | } \hline x & - 4 & - 2 & 2 & 4 & 6 & 8 \\\hline f ^ { - 1 } ( x ) & - 3 & - 2 & 0 & 1 & 8 & 3 \\\hline\end{array}$$
B) $$\begin{array} { | l | l | l | l | l | l | l | } \hline x & - 4 & - 2 & 2 & 4 & 6 & 6 \\\hline f ^ { - 1 } ( x ) & - 2 & - 2 & 0 & 1 & 2 & 3 \\\hline\end{array}$$
C) $$\begin{array} { | l | l | l | l | l | l | l | } \hline x & - 4 & - 2 & 2 & 4 & 6 & 8 \\\hline f ^ { - 1 } ( x ) & - 3 & 0 & 1 & 1 & 8 & 3 \\\hline\end{array}$$
D) $$\begin{array} { | l | l | l | l | l | l | l | } \hline x & - 4 & - 2 & 2 & 4 & 6 & 8 \\\hline f ^ { - 1 } ( x ) & - 3 & - 2 & 0 & 6 & 2 & 3 \\\hline\end{array}$$
E) $$\begin{array} { | l | l | l | l | l | l | l | } \hline x & - 4 & - 2 & 2 & 4 & 6 & 8 \\\hline f ^ { - 1 } ( x ) & - 3 & - 2 & 0 & 1 & 2 & 3 \\\hline\end{array}$$

Question 21

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1. ​
F(x)= |x - 9| + 1
​

A)f^-1(x)= x + 8 The domain of f and the range of f^-1 are all real numbers x such that x ≥ 9.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 1.
B)f^-1(x)= x - 8 The domain of f and the range of f^-1 are all real numbers x such that x ≥ 9.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 1.
C)f^-1(x)= -x - 8 The domain of f and the range of f^-1 are all real numbers x such that x ≥ 1.The domain of f^-1 and the range of f are all real numbers x such that x ≥ -9.
D)f^-1(x)= x + 8 The domain of f and the range of f^-1 are all real numbers x such that x ≥ -9.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 1.
E)f^-1(x)= -x + 8 The domain of f and the range of f^-1 are all real numbers x such that x ≥ 1.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 9.

Question 22

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1. ?
F(x)= -6x² + 2
?

A) $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { 6 }$ The domain of f and the range of f^-1 are all real numbers x such that x ? 0.The domain of f^-1 and the range of f are all real numbers x such that x ? 2.?
B) $f ^ { - 1 } ( x ) = \frac { \sqrt { - 2 ( x - 6 ) } } { 2 }$ The domain of f and the range of f^-1 are all real numbers x such that x ? 0.The domain of f^-1 and the range of f are all real numbers x such that x ? 2.?
C) $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { - 6 }$ The domain of f and the range of f^-1 are all real numbers x such that x ? 0.The domain of f^-1 and the range of f are all real numbers x such that x ? 2.?
D) $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { 6 }$ The domain of f and the range of f^-1 are all real numbers x such that x ? 0.The domain of f^-1 and the range of f are all real numbers x such that x ? -2.?
E) $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x + 2 ) } } { 6 }$ The domain of f and the range of f^-1 are all real numbers x such that x ? 0.The domain of f^-1 and the range of f are all real numbers x such that x ? 2.

Question 23

Determine whether the function has an inverse function.If it does,find the inverse function. ?
F(x)= (x + 4)²,x ? -4
?

A) $f ^ { - 1 } ( x ) = \sqrt { x } + 4$
B)f^-1(x)= -(x + 4)²
C)f^-1(x)= (x + 4)^-2
D)? $f ^ { - 1 } ( x ) = \sqrt { x } - 4$
E)No inverse

Question 24

Your wage is $11.00 per hour plus $0.50 for each unit produced per hour.So,your hourly wage in terms of the number of units produced x is y = 11 + 0.50x.Find the inverse function.What does each variable represent in the inverse function? ?

A) $y = \frac { x - 11 } { 0.50 }$ x = hourly wage;y = numbers of units produced
B)y = 11 + 0.50x x = hourly wage;y = numbers of units produced
?
C) $$y = \frac { x + 11 } { 0.50 }$$ x = hourly wage;y = numbers of units produced
?
D) $y = \frac { 11 - x } { 0.50 }$ x = hourly wage;y = numbers of units produced
?
E)y = 11 - 0.50x x = hourly wage;y = numbers of units produced
?

Question 25

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1. ?
F(x)= (x - 5)²
?

A) $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ ?
The domain of f and the range of f^-1 are all real numbers x such that x ? 5.The domain of f^-1 and the range of f are all real numbers x such that x ? 0.
B) $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ ?
The domain of f and the range of f^-1 are all real numbers x such that x ? 0.The domain of f^-1 and the range of f are all real numbers x such that x ? -5.
C) $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ ?
The domain of f and the range of f^-1 are all real numbers x such that x ? 5.The domain of f^-1 and the range of f are all real numbers x such that x ? 0.
D) $f ^ { - 1 } ( x ) = \sqrt { x } + 5$ ?
The domain of f and the range of f^-1 are all real numbers x such that x ? 0.The domain of f^-1 and the range of f are all real numbers x such that x ? 5.
E) $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ ?
The domain of f and the range of f^-1 are all real numbers x such that x ? -5.The domain of f^-1 and the range of f are all real numbers x such that x ? 0.

Question 26

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x)= x³ to find (f^-1 _º f^-1)(-5). ?

A)36
B)44
C)40
D)38
E)42

Question 27

Use the functions given by f(x)= x + 6 and g(x)= 7x - 3 to find g^-1 _º f^-1. ?

A) $\frac { - x - 3 } { 7 }$
B) $\frac { x + 3 } { 7 }$
C) $\frac { x - 3 } { 7 }$
D) $\frac { x - 3 } { - 7 }$
E) $\frac { x - 7 } { 3 }$

Question 28

Determine whether the function has an inverse function.If it does,find the inverse function.? $h ( x ) = - \frac { 4 } { x ^ { 2 } }$ ?

A) $h ^ { - 1 } ( x ) = \frac { 4 } { x ^ { 2 } }$
B) $h ^ { - 1 } ( x ) = - \frac { x ^ { 2 } } { 4 }$
C) $h ^ { - 1 } ( x ) = - \frac { 4 } { x ^ { 2 } }$
D) $h ^ { - 1 } ( x ) = \frac { x ^ { 2 } } { 4 }$
E)No inverse

Question 29

Use the functions given by $f ( x ) = \frac { 1 } { 125 } x - 1$ and g(x)= x³ to find (f _º g)^-1. ?

A) $5 \sqrt [ 3 ] { x - 1 }$
B) $125 \sqrt [ 3 ] { x - 1 }$
C) $5 \sqrt [ 3 ] { x + 1 }$
D) $125 \sqrt [ 3 ] { x + 1 }$
E) $5 \sqrt { x + 1 }$

Question 30

Use the functions given by $f ( x ) = \frac { 1 } { 64 } x - 4$ and g(x)= x³ to find g^-1 _º f^-1. ?

A) $4 \sqrt [ 3 ] { ( 4 - x ) }$
B) $- 4 \sqrt [ 3 ] { ( x + 4 ) }$
C) $- 4 \sqrt [ 3 ] { ( x - 4 ) }$
D) $4 \sqrt [ 3 ] { ( x - 4 ) }$
E) $4 \sqrt [ 3 ] { ( x + 4 ) }$

Question 31

Determine whether the function has an inverse function.If it does,find the inverse function.? $f ( x ) = \sqrt { 7 x + 8 }$ ?

A) $f ^ { - 1 } ( x ) = - \frac { x ^ { 2 } + 8 } { 7 }$
B) $f ^ { - 1 } ( x ) = - \frac { x ^ { 2 } - 8 } { 7 }$
C) $f ^ { - 1 } ( x ) = \frac { x ^ { 2 } - 8 } { 7 }$
D) $f ^ { - 1 } ( x ) = \frac { x ^ { 2 } + 8 } { 7 }$
E)No Inverse

Question 32

Determine whether the function has an inverse function.If it does,find the inverse function. ?
F(x)= -2
?

A)f^-1(x)= 2
B) $f ^ { - 1 } ( x ) = - \frac { 1 } { 2 }$
C) $f ^ { - 1 } ( x ) = \frac { 1 } { 2 }$
D)f^-1(x)= -2
E)No inverse

Question 33

Determine whether the function has an inverse function.If it does,find the inverse function.? $g ( x ) = \frac { x } { 5 }$ ?

A) $g ^ { - 1 } ( x ) = - 5 x$
B) $g ^ { - 1 } ( x ) = 5 x$
C) $$g ^ { - 1 } ( x ) = \frac { 5 } { x }$$
D) $g ^ { - 1 } ( x ) = - \frac { x } { 5 }$
E)No inverse

Question 34

Use the functions given by f(x)= x + 2 and g(x)= 2x - 5 to find (f _º g)^-1. ?

A) $\frac { x + 3 } { 2 }$
B) $\frac { x - 3 } { - 2 }$
C) $\frac { x - 4 } { 3 }$
D) $\frac { x - 3 } { 2 }$
E) $\frac { - x - 3 } { 2 }$

Question 35

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1. ​
F(x)= |x + 5|
​

A)f​^-1(x)= x - 5 ​
The domain of f and the range of f^-1 are all real numbers x such that x ≥ -5.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 0.
B)f​^-1(x)= x + 5 ​
The domain of f and the range of f^-1 are all real numbers x such that x ≥ 0.The domain of f^-1 and the range of f are all real numbers x such that x ≥ -5.
C)f​^-1(x)= x - 5 ​
The domain of f and the range of f^-1 are all real numbers x such that x ≥ 0.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 5.
D)f​^-1(x)= x + 5 ​
The domain of f and the range of f^-1 are all real numbers x such that x ≥ 5.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 0.
E)f​^-1(x)= x - 5 ​
The domain of f and the range of f^-1 are all real numbers x such that x ≥ 5.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 0.

Question 36

?Use the graph of the function f to create a table of values for the given points.Then create a second table that can be used to find f^-1. ?? ?

A) $$\begin{array}{l}\begin{array} { | l | l | l | l | l | } \hline x & 1 & 4 & 7 & 8 \\\hline y & 1 & 4 & 7 & 9 \\\hline\end{array}\\\\\begin{array} { | l | l | l | l | l | } \hline x & 1 & 4 & 7 & 9 \\\hline f ^ { - 1 } ( x ) & 1 & 4 & 7 & 8 \\\hline\end{array}\end{array}$$
B) $$\begin{array}{l}\begin{array} { | l | l | l | l | l | } \hline x & 1 & 4 & 7 & 9 \\\hline y & 1 & 4 & 7 & 8 \\\hline\end{array}\\\\\begin{array} { | l | l | l | l | l | } \hline x & 1 & 4 & 7 & 8 \\\hline f ^ { - 1 } ( x ) & 1 & 4 & 7 & 9 \\\hline\end{array}\end{array}$$
C) $$\begin{array}{l}\begin{array} { | l | l | l | l | l | } \hline x & 1 & 4 & 7 & 8 \\\hline y & 1 & 4 & 7 & 9 \\\hline\end{array}\\\\\begin{array} { | l | l | l | l | l | } \hline x & 1 & 4 & 7 & 9 \\\hline f ^ { - 1 } ( x ) & - 1 & - 4 & - 7 & - 8 \\\hline\end{array}\end{array}$$
D) $$\begin{array}{l}\begin{array} { | l | l | l | l | l | } \hline x & - 1 & - 4 & - 7 & - 9 \\\hline y & 1 & 4 & 7 & 8 \\\hline\end{array}\\\\\begin{array} { | l | l | l | l | l | } \hline x & 1 & 4 & 7 & 8 \\\hline f ^ { - 1 } ( x ) & 1 & 4 & 7 & 9 \\\hline\end{array}\end{array}$$
E) $$\begin{array}{l}\begin{array} { | l | l | l | l | l | } \hline x & - 1 & - 4 & - 7 & - 9 \\\hline y & 1 & 4 & 7 & 8 \\\hline\end{array}\\\\\begin{array} { | l | l | l | l | l | } \hline x & 1 & 4 & 7 & 9 \\\hline f ^ { - 1 } ( x ) & - 1 & - 4 & - 7 & - 8 \\\hline\end{array}\end{array}$$

Question 37

The function given by y = 0.03x² + 245.50,0 < x < 100 approximates the exhaust temperature y in degrees Fahrenheit,x where is the percent load for a diesel engine.Find the inverse function. ?

A) $y = \frac { x + 245.50 } { - 0.03 }$
B) $y = \sqrt { \frac { x - 245.50 } { 0.03 } }$
C) $y = \frac { x - 245.50 } { 0.03 }$
D) $y = \sqrt { \frac { x + 245.50 } { 0.03 } }$
E) $y = \frac { x + 245.50 } { 0.03 }$

Question 38

Determine whether the function has an inverse function.If it does,find the inverse function.? f ( x ) = \left\{ \begin{array} { l } x + 2 , x < 0 \\2 - x , x \geq 0\end{array} \\) ?</strong><div>A) \(f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 2 + x , x \geq 0 \\x - 2 , x < 0\end{array} \right. .

B) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 2 + x , x \geq 0 \\x - 2 , x < 0\end{array} \right.$

C) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } x - 2 , x \geq 0 \\2 + x , x < 0\end{array} \right.$

D) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } x + 2 , x \geq 0 \\2 - x , x < 0\end{array} \right.$ .

E)No inverse

Question 39

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x)= x³ to find (g^-1 _º f^-1)(-5). ?

A)-2
B)0
C)-4
D)2
E)4

Question 40

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 1$ and g(x)= x³ to find (f^-1 _º g^-1)(1). ?

A)14
B)12
C)16
D)20
E)18

Question 41

Find the inverse of the one-to-one function.? $y = \frac { 1 } { 8 x }$ ?

A) $f ^ { - 1 } ( x ) = \frac { 8 } { x }$
B) $f ^ { - 1 } ( x ) = \frac { x } { 8 }$
C) $f ^ { - 1 } ( x ) = 8 x$
D) $f ^ { - 1 } ( x ) = \frac { 1 } { 8 x }$
E)inverse does not exist

Question 42

Find the inverse of the one-to-one function. ?
Y = 3x
?

A) $f ^ { - 1 } ( x ) = 3 x ^ { 2 }$
B)f ^-1(x)= 3x
C) $f ^ { - 1 } ( x ) = \frac { x } { 3 }$
D) $f ^ { - 1 } ( x ) = \frac { 3 } { x }$
E)f ^-1(x)= 9x

Question 43

Find the inverse of the one-to-one function.
​
y = 6x
​
f ^-1(x)= __________

Question 44

Restrict the domain of f(x)= x² + 5 to x ≥ 0.Use a graphing utility to graph the function. ​

A)​
B)
C)​
D)​
E)

Question 45

Find the inverse of the one-to-one function. ?
Y = 5x + 9
?

A) $f ^ { - 1 } ( x ) = \frac { x + 9 } { 5 }$
B) $f ^ { - 1 } ( x ) = \frac { x - 9 } { 5 }$
C) $f ^ { - 1 } ( x ) = \frac { 5 } { x - 9 }$
D) $f ^ { - 1 } ( x ) = \frac { x - 5 } { 9 }$
E)none of the above

Question 46

Show algebraically that f and g are inverse functions.
f(x)= 9x + 9

Question 47

Find the inverse of the one-to-one function.
​
y = 5x + 4
​
f ^-1(x)= __________

Question 48

Consider the functions given by f(x)= x + 3 and f^-1(x)= x - 3.Evaluate f(f^-1(x))and f^-1(f(x))for the indicated values of x.What can you conclude about the functions
$$\begin{array} { | l | l | l | l | l | } \hline x & - 1 & 0 & 4 & 49 \\\hline f \left( f ^ { - 1 } ( x ) \right) & & & & \\\hline f ^ { - 1 } ( f ( x ) ) & & & & \\\hline\end{array}$$

A) $$\begin{array} { | l | l | l | l | l | } \hline x & - 1 & 0 & 4 & 49 \\\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & - 4 & - 49 \\\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & 4 & 49 \\\hline\end{array}$$ We can conclude that, both the functions have the same value for negative variables
B) $$\begin{array} { | l | l | l | l | l | } \hline x & - 1 & 0 & 4 & 49 \\\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & 4 & 49 \\\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & 4 & 49 \\\hline\end{array}$$ We can conclude that, both the functions have the same value
C) $$\begin{array} { | l | l | l | l | l | } \hline x & - 1 & 0 & 4 & 49 \\\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & 4 & 49 \\\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & - 4 & - 49 \\\hline\end{array}$$ We can conclude that, both the functions have the same value for negative variables.
D) $$\begin{array} { | l | l | l | l | l | } \hline x & - 1 & 0 & 4 & 49 \\\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & - 4 & 49 \\\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & 4 & - 49 \\\hline\end{array}$$ We can conclude that, both the functions are opposite of each other.
E) $$\begin{array} { | l | l | l | l | l | } \hline x & - 1 & 0 & 4 & 49 \\\hline f \left( f ^ { - 1 } ( x ) \right) & - 1 & 0 & 4 & - 49 \\\hline f ^ { - 1 } ( f ( x ) ) & - 1 & 0 & - 4 & 49 \\\hline\end{array}$$
We can conclude that, both the functions are opposite of each other.

Question 49

Graph the given function. f(x)= (x - 3)²

A)
B)
C)
D)
E)

Question 50

Find the inverse of the one-to-one function.​ ​
f ^-1(x)= __________

Question 51

Show algebraically that f and g are inverse functions. ,x ≥ 8 g(x)= x² + 8,x ≥ 0

Question 52

Determine algebraically whether f and g are inverse functions. f(x)= 5x - 3 $g ( x ) = \frac { x + 3 } { 5 }$

A)Yes,f and g are inverse functions. $f ( g ( x ) ) = f \left( \frac { x + 3 } { 5 } \right) = 5 \left( \frac { x + 3 } { 5 } \right) - 3 = x + 3 - 3 = x$ $g ( f ( x ) ) = g ( 5 x - 3 ) = \frac { 5 x - 3 + 3 } { 5 } = \frac { 5 x } { 5 } = x$
B)No,f and g are not inverse functions. $f ( g ( x ) ) = f \left( \frac { x + 3 } { 5 } \right) = 5 \left( \frac { x + 3 } { 5 } \right) - 3 = x + 3 - 3 = x$ $g ( f ( x ) ) = g ( 5 x - 3 ) = \frac { 5 x - 3 + 3 } { 5 } = \frac { 5 x } { 5 } = - x$

Question 53

The function f(x)= x² - 2 is one-to-one on the domain (x ? 0).Find f ^-1(x). ?

A) $f ^ { - 1 } ( x ) = - \sqrt { x + 2 }$
B) $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 2 } - 2 }$
C) $f ^ { - 1 } ( x ) = \sqrt { x + 2 }$
D) $f ^ { - 1 } ( x ) = \sqrt { x - 2 }$
E)f ^-1(x)= x² + 2

Question 54

Determine whether the function has an inverse function.If it does,find the inverse function. f(x)= x² + 5

A) $$f ^ { - 1 } ( x ) = \sqrt { x } + 5 , x \geq 0$$
B) $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$
C) $f ^ { - 1 } ( x ) = \sqrt { x } - 5$
D) $f ^ { - 1 } ( x ) = \sqrt { x + 5 } , x \geq - 5$
E)No inverse function exists.

Question 55

Determine whether the function is one-to- one. ​
Y = 3x
​

A)No,it isn't one-to-one.
B)Yes,it is one-to-one.

Question 56

Determine algebraically whether f and g are inverse functions. $f ( x ) = \sqrt { x + 6 }$ g(x)= x² - 6,x ? 0

A)Yes,f and g are inverse functions. $f ( g ( x ) ) = f \left( x ^ { 2 } - 6 \right) = \sqrt { \left( x ^ { 2 } - 6 \right) + 6 } = \sqrt { x ^ { 2 } } = x$ $g ( f ( x ) ) = g ( \sqrt { x + 6 } ) = ( \sqrt { x + 6 } ) ^ { 2 } - 6 = x + 6 - 6 = x$
B)No,f and g are not inverse functions. $f ( g ( x ) ) = f \left( x ^ { 2 } - 6 \right) = \sqrt { \left( x ^ { 2 } - 6 \right) + 6 } = \sqrt { x ^ { 2 } } = x$ $g ( f ( x ) ) = g ( \sqrt { x + 6 } ) = ( \sqrt { x + 6 } ) ^ { 2 } - 6 = - x + 6 - 6 = - x$

Question 57

?Use the functions given by $f ( x ) = \frac { x } { 8 } - 1$ and g(x)= x³ to find the indicated value. (f _º g)^-1(5)

A)? $- \frac { 387 } { 512 }$
B)? $2 \sqrt [ 3 ] { 6 }$
C)? $- 2 \sqrt [ 3 ] { 6 }$
D)? $2 \sqrt [ 3 ] { 4 }$
E)?Undefined

Question 58

Determine whether the function has an inverse function.If it does,find the inverse function. $f ( x ) = \left\{ \begin{array} { l } 8 x + 13 , x < - 2 \\( x + 2 ) ^ { 2 } - 3 , x \geq - 2\end{array} \right.$

A) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } \frac { x - 13 } { 8 } , x < - 2 \\\\\sqrt { x + 3 } - 2 , x \geq - 2\end{array} \right.$
B)? $$f ^ { - 1 } ( x ) = \left\{ \begin{array} { c } \frac { x - 13 } { 8 } , x < - 2 \\\\\sqrt { x + 1 } , x \geq - 2\end{array} \right.$$
C) $$f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } \frac { x - 13 } { 8 } , x < - 3 \\\\\sqrt { x + 3 } - 2 , x \geq - 3\end{array} \right.$$
D) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } \frac { x + 13 } { 8 } , x < - 3 \\\\\sqrt { x + 3 } - 2 , x \geq - 3\end{array} \right.$
E)No inverse function exists.

Question 59

Determine whether the function is one-to-one. ​
Y = (x - 5)²;x ≥ 5
​

A)No,it isn't one-to-one.
B)Yes,it is one-to-one.