Deck 8: Combinations of Functions Composite Functions

Question 1

​Find $g \circ g$ .​ $g ( x ) = x - 2$ ​

A) $$( x - 2 ) ^ { 2 }$$
B) $x ^ { 2 } - 2$
C) $x + 4$
D) $- x - 4$
E) $x - 4$

Answer 1

$x - 4$

Question 2

Find $( f - g ) ( x )$ .​ $f ( x ) = x ^ { 2 } + 3 , g ( x ) = \sqrt { 5 - x }$ ​

A) $x ^ { 2 } + 3 + \sqrt { 5 - x }$
B) $x ^ { 2 } - 3 + \sqrt { 5 - x }$
C) $x ^ { 2 } - 3 + \sqrt { 5 + x }$
D) $x ^ { 2 } + 3 - \sqrt { 5 - x }$
E) $x ^ { 2 } - 3 - \sqrt { 5 - x }$

Answer 2

$x ^ { 2 } + 3 - \sqrt { 5 - x }$

Question 3

Find $( f g ) ( x )$ .​ $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }$ ​

A) $\frac { 1 } { x ^ { 4 } }$
B) $\frac { 1 } { x ^ { 2 } }$
C) $\frac { 1 } { x ^ { 6 } }$
D) $x ^ { 6 }$
E) $\frac { x ^ { 4 } } { x ^ { 2 } }$

Answer 3

$\frac { 1 } { x ^ { 6 } }$

Question 4

​Find $g \circ f$ .​ $f ( x ) = x ^ { 2 } , g ( x ) = x - 4$ ​ ​

A) $x ^ { 2 } - 4$
B) $x ^ { 2 }$
C) $( x - 4 ) ^ { 2 }$
D) $\left( x ^ { 2 } + 4 \right)$
E) $( x + 4 ) ^ { 2 }$

Question 5

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 3$ and $g ( x ) = x - 4$ .​ $( f - g ) ( 3 t )$ ​ ​

A) $9 t ^ { 2 } + 3 t + 7$
B) $6 t + 7$
C) $9 t ^ { 2 } + 3 t - 7$
D) $9 t ^ { 2 } - 3 t - 7$
E) $9 t ^ { 2 } - 3 t + 7$

Question 6

Find (f + g)(x).​ $$f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { 7 - x }$$ ​

A) $$x ^ { 2 } + 4 - \sqrt { 7 - x }$$
B) $x ^ { 2 } + 4 + \sqrt { 7 - x }$
C) $x ^ { 2 } - 4 + \sqrt { 7 + x }$
D) $x ^ { 2 } - 4 - \sqrt { 7 - x }$
E) $x ^ { 2 } - 4 + \sqrt { 7 - x }$

Question 7

Find (f / g)(x).What is the domain of f / g?​ $$f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 3$$ ​

A) $$- \frac { x ^ { 2 } } { 7 x - 3 }$$ ;all real numbers x.
B) $\frac { 7 x + 3 } { x ^ { 2 } }$ ;all real numbers x except x = 0
C) $\frac { x ^ { 2 } } { 7 x - 3 }$ ;all real numbers x except x = $\frac { 3 } { 7 }$
D) $\frac { 7 x - 3 } { x ^ { 2 } }$ ;all real numbers x except x = 0
E) $\frac { x ^ { 2 } } { 7 x + 3 }$ ;all real numbers x except x = $\frac { 7 } { 3 }$

Question 8

Find (f + g)(x).​ $$f ( x ) = 2 x - 3 , g ( x ) = 4 - x$$ ​

A) $$3 x - 1$$
B) $2 x - 1$
C) $$2 x + 1$$
D) $3 x + 1$
E) $x + 1$

Question 9

​​​Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 6$ and $g ( x ) = x - 5$ .​ $( f / g ) ( - 4 ) - g ( 6 )$ ​ ​

A) $- \frac { 5 } { 26 }$
B) $- \frac { 31 } { 9 }$
C) $- \frac { 9 } { 13 }$
D) $- \frac { 13 } { 9 }$
E) $- \frac { 9 } { 31 }$

Question 10

​​Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 5$ and $g ( x ) = x - 4$ .​ $( f / g ) ( 5 )$ ​ ​

A)30
B) $\frac { 5 } { 34 }$
C) $\frac { 32 } { 3 }$
D) $\frac { 2 } { 31 }$
E) $\frac { 34 } { 5 }$

Question 11

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 2$ and $g ( x ) = x - 4$ .​ $( f + g ) ( 3 )$ ​

A)12
B)-10
C)7
D)14
E)10

Question 12

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 3$ and $g ( x ) = x - 6$ .​ $( f - g ) ( 0 )$ ​ ​

A)48
B)39
C)9
D)0
E)-39

Question 13

Find (f + g)(x).​ $$f ( x ) = x + 4 , g ( x ) = x - 4$$ ​

A)2x
B)4x
C)-4x
D)-2x
E)2x + 8

Question 14

​Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 5$ and $g ( x ) = x - 2$ .​ $( f g ) ( 5 )$ ​ ​

A)92
B)90
C)-86
D)89
E)91

Question 15

Find $( f / g ) ( x )$ .​ $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }$ ​

A) $\frac { 1 } { x ^ { 2 } }$
B) $x ^ { 6 }$
C) $\frac { 1 } { x ^ { 4 } }$ ​
D) $\frac { 1 } { x ^ { 6 } }$
E) $x ^ { 2 }$

Question 16

Find (f - g)(x).​ $$f ( x ) = 2 x - 2 , g ( x ) = 4 - x$$ ​

A) $3 x - 6$
B) $2 x + 6$
C) $2 x - 6$
D) $x - 6$
E) $3 x + 6$

Question 17

Find (f - g)(x).​ $$f ( x ) = x + 3 , g ( x ) = x - 3$$ ​

A)2x - 6
B)6
C)2x - 3
D)2x + 6
E)2x

Question 18

Find (fg)(x).​ $$f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 7$$ ​

A) $$7 x ^ { 3 } + 7 x ^ { 2 }$$
B) $7 x ^ { 3 } - 7 x ^ { 2 }$
C) $7 x ^ { 2 } - 7 x ^ { 3 }$
D) $7 x ^ { 2 } + 7 x ^ { 3 }$
E) $7 x - 7 x ^ { 2 }$

Question 19

Find $f \circ g$ .​ $f ( x ) = x ^ { 2 } , g ( x ) = x - 2$ ​

A) $x ^ { 2 }$
B) $( x - 2 ) ^ { 2 }$
C) $( x + 2 ) ^ { 2 }$
D) $\left( x ^ { 2 } - 2 \right)$
E) $\left( x ^ { 2 } + 2 \right)$

Question 20

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 2$ and $g ( x ) = x - 6$ .​ $( f - g ) ( - 5 )$ ​ ​

A)28
B)38
C)-38
D)125
E)17

Question 21

The number N of bacteria in a refrigerated food is given by $N ( T ) = 10 T ^ { 2 } - 20 T + 600,1 \leq T \leq 20$ where T is the temperature of the food in degrees Celsius.When the food is removed from refrigeration,the temperature of the food is given by $T ( t ) = 3 t + 2,0 \leq t \leq 6$ where t is the time in hours. Find the bacteria count after 0.5 hour.
​

A)About 565 bacteria
B)About 793 bacteria
C)About 653 bacteria
D)About 390 bacteria
E)About 705 bacteria

Question 22

Determine whether the statement is true or false. ​
If f(x)= x + 1 and g(x)= 5x,then $( f \circ g ) ( x ) = ( g \circ f ) ( x )$ .
​

A)False
B)True

Question 23

Consider the functions $f ( x ) = x ^ { 3 }$ and $g ( x ) = \sqrt { x }$ . ​
Find $f / g$ .
​

A) $x ^ { 3 } \sqrt { x }$
B) $\frac { \sqrt { x } } { x ^ { 2 } }$
C) $\frac { \sqrt { x } } { x ^ { 3 } }$
D) $\frac { x ^ { 2 } \sqrt { x } } { x }$
E) $x ^ { 2 } \sqrt { x }$

Question 24

Find $f \circ g$ and the domain of the composite function.​ $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 7$ ​

A) $\frac { 1 } { x } + 7$ Domain of $f \circ g$ : all real numbers x except $x = 0$
B) $- \frac { 1 } { x + 7 }$ Domain of $f \circ g$ : all real numbers x except $x = - 7$
C) $\frac { 1 } { x + 7 }$ Domain of $f \circ g$ : all real numbers x except $x = - 7$
D) $\frac { 1 } { x } - 7$ Domain of $f \circ g$ : all real numbers x except $x = 0$
E) $\frac { 1 } { x - 7 }$ Domain of $f \circ g$ : all real numbers x except $x = 7$

Question 25

Find $g \circ f$ and the domain of the composite function.​ $f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { x }$ ​

A) $( x + 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x
B) $( x - 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x
C) $\sqrt { x ^ { 2 } + 4 }$ Domain of $g \circ f$ : all real numbers x
D) $\sqrt { ( x - 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x
E) $\sqrt { ( x + 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x

Question 26

A pebble is dropped into a calm pond,causing ripples in the form of concentric circles.The radius (in feet)of the outer ripple is $r ( t ) = 0.2 t$ ,where t is the time in seconds after the pebble strikes the water.The area of the circle is given by the function $A ( r ) = \pi r ^ { 2 }$ .Find and interpret $( A \circ r ) ( t )$ . ​

A) $$( A \circ r ) ( t ) = 0.2 \pi t$$ ; $$( A \circ r ) ( t )$$ represents the area of the circle at time t.
B) $( A \circ r ) ( t ) = 0.2 \pi t ^ { 2 }$ ; $( A \circ r ) ( t )$ represents the area of the circle at time t.
C) $$( A \circ r ) ( t ) = 0.04 \pi t$$ ; $( A \circ r ) ( t )$ represents the area of the circle at time t.
D) $( A \circ r ) ( t ) = 0.04 \pi t ^ { 2 }$ ; $$( A \circ r ) ( t )$$ represents the area of the circle at time t.
E) $$( A \circ r ) ( t ) = 0.04 \pi t ^ { 3 }$$ ; $( A \circ r ) ( t )$ represents the area of the circle at time t.

Question 27

From 2003 through 2008,the sales $R _ { 1 }$ (in thousands of dollars)for one of two restaurants owned by the same parent company can be modeled by​ $R _ { 1 } = 480 - 6 t - 0.6 t ^ { 2 } , t = 3,4,5,6,7,8$ ​ where t = 3 represents 2003.During the same six-year period,the sales $R _ { 2 }$ (in thousands of dollars)for the second restaurant can be modeled by​ $R _ { 2 } = 259 + 0.77 t , t = 3,4,5,6,7,8$ ​
Write a function $R _ { 3 }$ that represents the total sales of the two restaurants owned by the same parent company.
​

A)​ $R _ { 3 } = 739 - 5.23 t ^ { 2 } - 0.6 t$
B)​ $$R _ { 3 } = 739 - 5.23 t + 0.6 t ^ { 2 }$$
C)​ $$R _ { 3 } = 221 - 6.77 t ^ { 2 } - 0.6 t$$
D)​ $R _ { 3 } = 739 - 5.23 t ^ { 2 } + 0.6 t$
E)​ $R _ { 3 } = 739 - 5.23 t - 0.6 t ^ { 2 }$

Question 28

The spread of a contaminant is increasing in a circular pattern on the surface of a lake.The radius of the contaminant can be modeled by $r ( t ) = 2.25 \sqrt { t }$ ,where r is the radius in meters and t is the time in hours since contamination. ​
Find a function that gives the area A of the circular lake in terms of the time since the spread began.
​

A) $A \circ r ( t ) = 5.0625 \pi \sqrt { t }$
B) $A \circ r ( t ) = 2.25 \pi t$
C) $A \circ r ( t ) = 5.0625 t$
D) $A \circ r ( t ) = 5.0625 \sqrt { t }$
E) $A \circ r ( t ) = 5.0625 \pi t$

Question 29

​Find $g \circ f$ and the domain of the composite function.​ $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 5$ ​

A) $\frac { 1 } { x + 5 }$ Domain of $g \circ f$ : all real numbers x except $x = - 5$
B) $\frac { 1 } { x } - 5$ Domain of $g \circ f$ : all real numbers x except $x = 0$
C) $\frac { 1 } { x } + 5$ Domain of $g \circ f$ : all real numbers x except $x = 0$
D) $- \frac { 1 } { x + 5 }$ Domain of $g \circ f$ : all real numbers x except $x = - 3$
E) $\frac { 1 } { x - 5 }$ Domain of $g \circ f$ : all real numbers x except $x = 5$

Question 30

Find $f \circ g$ and the domain of the composite function.​ $f ( x ) = | x | , g ( x ) = x + 3$ ​

A) $\left| ( x - 3 ) ^ { 3 } \right|$ Domain of $f \circ g$ : all real numbers x
B) $\sqrt { ( x + 3 ) ^ { 3 } }$ Domain of $f \circ g$ : all real numbers x
C) $| x + 3 |$ Domain of $f \circ g$ : all real numbers x
D) $\left| ( x + 3 ) ^ { 3 } \right|$ Domain of $f \circ g$ : all real numbers x
E) $| x - 3 |$ Domain of $f \circ g$ : all real numbers x

Question 31

The suggested retail price of a new hybrid car is p dollars.The dealership advertises a factory rebate of $2000 .
​
Select a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the factory.
​

A) $R ( p ) = 2000 - p$
B) $R ( p ) = p - 2000$
C) $R ( p ) = p + 2000$
D) $R ( p ) = p + 1000$
E) $R ( p ) = p - 1000$

Question 32

The weekly cost C of producing units x in a manufacturing process is given by $C ( x ) = 30 x + 750$ .The number of units x produced in t hours is given by $x ( t ) = 70 t$ . ​
Find the cost of the units produced in 6 hours.
​

A)11,855
B)11,850
C)11,846
D)13,350
E)11,854

Question 33

Find $g \circ f$ and the domain of the composite function.​ $f ( x ) = | x | , g ( x ) = x + 4$ ​ ​

A) $| x - 4 |$ Domain of $g \circ f$ : all real numbers x
B) $x - | 4 |$ Domain of $g \circ f$ : all real numbers x
C) $| x | - 4$ Domain of $g \circ f$ : all real numbers x
D) $| x | + 4$ Domain of $g \circ f$ : all real numbers x
E) $| x + 4 |$ Domain of $g \circ f$ : all real numbers x

Question 34

The number of people playing tennis T (in millions)in the United States from 2000 through 2007 can be approximated by the function​ $T ( t ) = 0.0235 t ^ { 4 } - 0.3401 t ^ { 3 } + 2.556 t ^ { 2 } - 6.86 t + 23.8$ ​ and the U.S.population P (in millions)from 2000 through 2007 can be approximated by the function $P ( t ) = 5.8 t + 224.5$ ,where t represents the year,with t = 0 corresponding to 2000.
Evaluate the function $h ( t ) = \frac { 0.0235 t ^ { 4 } - 0.3401 t ^ { 3 } + 2.556 t ^ { 2 } - 6.86 t + 23.8 } { 5.8 t + 224.5 }$ for t = 0 and 3.

A)h(0)= 0.1060,h(3)= 0.0783
B)h(0)= 0.3060,h(3)= 0.2783
C)h(0)= -0.2060,h(3)= -0.1783
D)h(0)= 0.1783,h(3)= 0.2060
E)h(0)= -0.1060,h(3)= -0.0783

Question 35

The total numbers of Navy personnel N (in thousands)and Marines personnel M (in thousands)from 2000 through 2007 can be approximated by the models​ $N ( t ) = 0.194 t ^ { 3 } - 7.88 t ^ { 2 } + 12.9 t + 375$ and $M ( t ) = 0.031 t ^ { 3 } - 0.25 t ^ { 2 } + 6.7 t + 173$ ​ where t represents the year,with t = 0 corresponding to 2000.
Find and interpret $( N - M ) ( t )$ .
​

A) $( N - M ) ( t ) = 0.163 t ^ { 3 } + 7.63 t ^ { 2 } - 6.2 t + 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel.
B) $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } - 6.2 t - 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel.
C) $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } - 6.2 t + 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel.
D) $( N - M ) ( t ) = 0.163 t ^ { 3 } + 7.63 t ^ { 2 } + 6.2 t + 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel.
E) $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } + 6.2 t + 202$ ,which represents the difference between the number of Navy personnel and the number of Marines personnel.

Question 36

The number of people playing tennis T (in millions)in the United States from 2000 through 2007 can be approximated by the function​ $T ( t ) = 0.0236 t ^ { 4 } - 0.3401 t ^ { 3 } + 6.556 t ^ { 2 } - 2.86 t + 26.8$ ​ and the U.S.population P (in millions)from 2000 through 2007 can be approximated by the function $P ( t ) = 5.78 t + 221.5$ ,where t represents the year,with t = 0 corresponding to 2000.
Find $h ( t ) = \frac { T ( t ) } { P ( t ) }$ .
​

A) $h ( t ) = \frac { 0.0236 t ^ { 4 } - 0.3401 t ^ { 3 } - 6.556 t ^ { 2 } - 2.86 t + 26.8 } { 5.78 t + 221.5 }$ ​
B) $h ( t ) = \frac { 0.0236 t ^ { 4 } - 0.3401 t ^ { 3 } + 6.556 t ^ { 2 } - 2.86 t + 26.8 } { 5.78 t + 221.5 }$ ​
C) $h ( t ) = \frac { 0.0236 t ^ { 4 } - 0.3401 t ^ { 3 } - 6.556 t ^ { 2 } - 2.86 t - 26.8 } { 5.78 t - 221.5 }$
D) $h ( t ) = \frac { 0.0236 t ^ { 4 } - 0.3401 t ^ { 3 } + 6.556 t ^ { 2 } - 2.86 t + 26.8 } { 5.78 t - 221.5 }$ ​
E) $h ( t ) = \frac { 0.0236 t ^ { 4 } + 0.3401 t ^ { 3 } + 6.556 t ^ { 2 } - 2.86 t + 26.8 } { 5.78 t + 221.5 }$

Question 37

The total numbers of Navy personnel N (in thousands)and Marines personnel M (in thousands)from 2000 through 2007 can be approximated by the models​ $N ( t ) = 0.193 t ^ { 3 } - 3.88 t ^ { 2 } + 15.9 t + 370$ and $M ( t ) = 0.033 t ^ { 3 } - 0.21 t ^ { 2 } + 1.7 t + 171$ ​ where t represents the year,with t = 0 corresponding to 2000.
​
Find and interpret $( N + M ) ( t )$ .
​

A) $( N + M ) ( t ) = 0.226 t ^ { 3 } + 4.09 t ^ { 2 } - 17.6 t - 541$ ,which represents the total number of Navy and Marines personnel combined.
B) $( N + M ) ( t ) = 0.226 t ^ { 3 } + 4.09 t ^ { 2 } + 17.6 t + 541$ ,which represents the total number of Navy and Marines personnel combined.
C) $( N + M ) ( t ) = 0.226 t ^ { 3 } - 4.09 t ^ { 2 } - 17.6 t - 541$ ,which represents the total number of Navy and Marines personnel combined.
D) $( N + M ) ( t ) = 0.226 t ^ { 3 } - 4.09 t ^ { 2 } + 17.6 t + 541$ ,which represents the total number of Navy and Marines personnel combined.
E) $( N + M ) ( t ) = 0.226 t ^ { 2 } - 4.09 t ^ { 3 } - 17.6 t + 541$ ,which represents the total number of Navy and Marines personnel combined.

Question 38

The research and development department of an automobile manufacturer has determined that when a driver is required to stop quickly to avoid an accident,the distance (in feet)the car travels during the driver's reaction time is given by $R ( x ) = \frac { 5 } { 2 } x$ ,where x is the speed of the car in miles per hour.The distance (in feet)traveled while the driver is braking is given by $B ( x ) = \frac { 1 } { 11 } x ^ { 2 }$ .Find the function that represents the total stopping distance T. ​

A) $T = - \frac { 5 } { 2 } x + \frac { 1 } { 11 } x ^ { 2 }$
B) $T = \frac { 5 } { 2 } x - \frac { 1 } { 11 } x ^ { 2 }$
C) $T = \frac { 5 } { 2 } x ^ { 2 } + \frac { 1 } { 11 } x ^ { 2 }$
D) $T = - \frac { 5 } { 2 } x - \frac { 1 } { 11 } x ^ { 2 }$
E) $T = \frac { 5 } { 2 } x + \frac { 1 } { 11 } x ^ { 2 }$

Question 39

Find $f \circ g$ and the domain of the composite function.​ $f ( x ) = \sqrt { x + 5 } , g ( x ) = x ^ { 2 }$ ​

A) $( x + 5 ) ^ { 2 }$ Domain of $f \circ g$ : all real numbers x
B) $\sqrt { x ^ { 2 } + 5 }$ Domain of $f \circ g$ : all real numbers x
C) $- \sqrt { ( x + 5 ) ^ { 2 } }$ Domain of $f \circ g$ : all real numbers x
D) $( x - 5 ) ^ { 2 }$ Domain of $f \circ g$ : all real numbers x
E) $\sqrt { ( x - 5 ) ^ { 2 } }$ Domain of $f \circ g$ : all real numbers x

Question 40

Find (f + g)(x).​​ $\begin{array} { l } f ( x ) = x ^ { 2 } - 2 x - 1 \\g ( x ) = - 3 x ^ { 2 } + x - 1\end{array}$ ​ ​

A)​ $( f + g ) ( x ) = 4 x ^ { 4 } - 3 x ^ { 2 }$
B)​ $( f + g ) ( x ) = 2 x ^ { 2 } - x + 2$
C)​ $( f + g ) ( x ) = - 2 x ^ { 4 } - x ^ { 2 } - 2$
D)​ $( f + g ) ( x ) = 4 x ^ { 2 } - 3 x$
E)​ $( f + g ) ( x ) = - 2 x ^ { 2 } - x - 2$

Question 41

Let .Find the composite function.​

Question 42

Let f (x)= 2x + 1,g(x)= 3x - 2.Find the function.​ $( f - g ) ( x )$ ​

A) $( f - g ) ( x ) = \frac { 2 x + 1 } { 3 x - 2 }$
B) $( f - g ) ( x ) = 3 - x$
C) $( f - g ) ( x ) = 6 x ^ { 2 } - x - 2$
D) $( f - g ) ( x ) = 5 x - 1$
E)none of the above

Question 43

Let f (x)= 2x - 1,g(x)= 3x - 2.Find the domain of the function.​ $( f + g ) ( x )$ ​

A) $( - \infty , \infty )$
B) $[ 0 , \infty )$
C) $( - \infty , 0 ]$
D) $( - \infty , 0 )$
E) $( 0 , \infty )$

Question 44

Use the graphs of f and g to evaluate the function. $( f \circ g ) ( 3 )$

A)1
B)-2
C)4
D)-1
E)2

Question 45

Find $f \circ g$ . $f ( x ) = - 2 x - 9 \quad g ( x ) = x + 5$

A) $( f \circ g ) ( x ) = - 2 x - 19$
B) $( f \circ g ) ( x ) = - 3 x - 14$
C) $( f \circ g ) ( x ) = - 2 x ^ { 2 } - 19 x - 45$
D) $( f \circ g ) ( x ) = - 3 x - 4$
E) $( f \circ g ) ( x ) = - 2 x - 4$

Question 46

Find ( fg )(x). $f ( x ) = \sqrt { 3 x } \quad g ( x ) = \sqrt { 5 x + 7 }$

A) $( f g ) ( x ) = \sqrt { 8 x + 7 }$
B) $( f g ) ( x ) = \sqrt { 15 x ^ { 2 } + 7 }$
C) $( f g ) ( x ) = \sqrt { 15 x ^ { 2 } + 21 x }$
D) $( f g ) ( x ) = x \sqrt { 15 } + \sqrt { 21 x }$
E) $( f g ) ( x ) = x \sqrt { 15 + 21 x }$

Question 47

Let f (x)= 3x,g (x)= x + 1.Find the composite function. ​​ ​
Please give the respnce as an expression (not an equation).

Question 48

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 7$ and $g ( x ) = x + 8$ .​ $( f - g ) ( t + 8 )$

A)​ $t ^ { 2 } + 15 t + 57$
B)​ $t ^ { 2 } + 15 t + 41$
C)​ $t ^ { 2 } + 17 t + 41$
D)​ $t ^ { 2 } - t + 41$
E)​ $t ^ { 2 } + 17 t + 57$

Question 49

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 6$ and $g ( x ) = x + 4$ . ( fg )(1)

A)15
B)-35
C)-23
D)-25
E)-33

Question 50

Find $f \circ g$ .​ $f ( x ) = \left| x ^ { 2 } + 1 \right| \quad g ( x ) = 9 - x$ ​

A) $$( f \circ g ) ( x ) = \left| x ^ { 2 } - 18 x + 82 \right|$$
B) $( f \circ g ) ( x ) = \left| x ^ { 2 } + 82 \right|$
C) $( f \circ g ) ( x ) = \left| 8 - x ^ { 2 } \right|$
D) $( f \circ g ) ( x ) = \left| 10 - x ^ { 2 } \right|$
E) $$( f \circ g ) ( x ) = 9 - \left| x ^ { 2 } + 1 \right|$$

Question 51

Let $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 5$ .Find the composite function which expresses the given correspondence correctly.​ $\frac { 1 } { x + 5 }$ ​

A) $$( g \circ g ) ( x )$$
B) $$( g \circ f ) ( x )$$
C) $( f \circ f ) ( x )$
D) $( f \circ g ) ( x )$
E)none of the above

Question 52

Let f (x)= x² - 1,g (x)= 3x - 2.Find the value of the function.​

Question 53

Find ( f / g )(x). $f ( x ) = x ^ { 2 } - 4 x \quad g ( x ) = 7 - x$ ​

A) $( f / g ) ( x ) = \frac { x ^ { 2 } - 4 x } { 7 - x } , x \neq 0$
B) $( f / g ) ( x ) = \frac { x - 4 } { 7 } , x \neq 0$
C) $( f / g ) ( x ) = \frac { x ^ { 2 } } { 7 } + 4 , x \neq 0$
D) $( f / g ) ( x ) = \frac { x ^ { 2 } - 4 x } { 7 - x } , x \neq 7$ ​
E) $( f / g ) ( x ) = \frac { x ^ { 2 } - 4 x } { 7 - x } , x \neq - 7$

Question 54

The monthly cost C of running the machinery in a factory for t hours is given by​ $C ( t ) = 40 t + 400$ The number of hours t needed to produce x products is given by $t ( x ) = 6 x$ . Find the equation representing the cost C of manufacturing x products.

A) $C ( x ) = 46 x + 440$
B) $C ( x ) = 240 x + 16,000$
C) $C ( x ) = 40 x + 406$
D) $C ( x ) = 46 x + 400$
E) $C ( x ) = 240 x + 400$ ​

Question 55

Let f (x)= 2x + 1,g (x)= 3x - 2.Find the function
Please give the responce as a simplified expression (not an equation).

Question 56

Find ( f − g )(x).​ $f ( x ) = - \frac { 6 x } { 7 x - 6 } \quad g ( x ) = - \frac { 4 } { x }$

A) $( f - g ) ( x ) = \frac { - 6 x + 34 } { 7 x - 6 }$
B) $( f - g ) ( x ) = \frac { - 6 x ^ { 2 } + 28 x + 24 } { 7 x ^ { 2 } - 6 x }$
C) $( f - g ) ( x ) = \frac { - 3 x + 2 } { 3 x - 3 }$
D) $( f - g ) ( x ) = \frac { - 6 x ^ { 2 } + 28 x - 24 } { 7 x ^ { 2 } - 6 x }$
E) $( f - g ) ( x ) = \frac { - 6 x + 22 } { 7 x - 6 }$

Question 57

Find $g \circ f$ .​ $f ( x ) = x - 9 \quad g ( x ) = x ^ { 2 }$ ​

A) $( g \circ f ) ( x ) = x ^ { 2 } - 18 x + 81$
B) $( g \circ f ) ( x ) = x ^ { 2 } - 81$
C) $( g \circ f ) ( x ) = x ^ { 2 } - 9 x + 81$ ​
D) $( g \circ f ) ( x ) = x ^ { 2 } - 9$
E) $( g \circ f ) ( x ) = x ^ { 2 } + 81$

Question 58

Find $f \circ g$ .​ $f ( x ) = x + 3 \quad g ( x ) = \frac { 1 } { x ^ { 2 } - 9 }$ ​

A) $( f \circ g ) ( x ) = \frac { 1 } { x ^ { 2 } }$
B) $( f \circ g ) ( x ) = \frac { 4 } { x ^ { 2 } - 9 }$
C) $( f \circ g ) ( x ) = \frac { 3 x ^ { 2 } - 2 } { x ^ { 2 } - 9 }$
D) $( f \circ g ) ( x ) = \frac { 1 } { x ^ { 2 } + 6 x }$
E) $( f \circ g ) ( x ) = \frac { 3 x ^ { 2 } - 26 } { x ^ { 2 } - 9 }$