Question 1

Find the absolute minimum value of the function.

Accepted Answer

The answer of Find the absolute minimum value of the...

Question 2

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 3

Find  if

Accepted Answer

The answer of Find  if ...

Question 4

Determine f(x) from the table. The values from the table are given to the nearest ten thousandth.      1    
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Determine f(x) from the table. The values...

Question 5

Determine whether the function is one-to-one. f (x) = 
A)No
B)Yes

Accepted Answer

The answer of Determine whether the function is one-to-one. f...

Question 6

Use logarithmic differentiation to find the derivative of the function. y = (x + 1)²(8x²- 5)³

Accepted Answer

The answer of Use logarithmic differentiation to find the derivative...

Question 7

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 8

Sketch a graph of the function.
f (x) =

Accepted Answer

The answer of Sketch a graph of the function.
f (x)...

Question 9

Differentiate the function.

Accepted Answer

The answer of Differentiate the function. ...

Question 10

If 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of If 
A) 
B) 
C) 
D) 
E) ...

Question 11

Find the inverse of the function. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the inverse of the function. 
A)...

Question 12

Suppose that g is the inverse of a function F. If f (3) = 4 and f '(3) = 5, find g'0(4).

A)4
B)3
C) 
D)

Accepted Answer

Since g is the inverse of F, we have $g(F(x))=x$. Therefore, $g(f^{-1}(3))=3$ and $g(f^{-1}(5))=5$. We know that $f(3)=4$, so $f^{-1}(4)=3$. Thus, $g(4) = g(f(f^{-1}(4))) = f^{-1}(4)$.
Similarly, we know that $f(f(f(3))) = f(5) = S'(3)$, so $g(S'(3)) = f(f(3))$. Finally, $f(f(3))=f(4)=10$.
Therefore, $g(4)=f^{-1}(4)=3$ and $g(S'(3))=f(f(3))=10,$ so the answer is D.

Question 13

Find the integral.

Accepted Answer

The answer of Find the integral. ...

Question 14

Find an equation of the tangent line to the curve at the given point.

Accepted Answer

The answer of Find an equation of the tangent line...

Question 15

Find f ^-¹(a) for the function f and the real number a. f (x) = x³ + x - 7; a = -5 A)0 B)3 C)2 D)1

Accepted Answer

The answer of Find f ^-¹(a) for the function...

Question 16

Find the inverse of F. Then sketch the graphs of f and f ^-¹ on the same set of axes.f (x) = , x $\ge$ 0 A)f ^-¹(x) = - , x $\ge$ 0 B)f ^-¹(x) = , x $\ge$ 0 C)f ^-¹(x) = , x $\ge$ 0 D)f ^-¹(x) = - , x $\ge$ 0

Accepted Answer

To find the inverse of f, we need to solve for x in terms of y. y = 11e^(x^2-5x-6) Taking the natural logarithm of both sides: ln(y) = (x^2-5x-6)ln(11) Solving for x using the quadratic formula: x = (5 +/- sqrt(25+4ln(y)ln(11))) / 2 Therefore, the inverse function is: f^-1(x) = (5 +/- sqrt(25+4ln(x)ln(11))) / 2 Now, to sketch the graph of f ^-¹ on the same set of axes as f, we can use the transformation rules: - f ¹ reflects f over the y-axis - f ^{shifts f left by 1 unit
- f} shifts the reflected function back over the y-axis - f ^{1 shifts the function up by 1 unit.
Overall, this transformation results in a new function with the same shape as f, but shifted to the left and up by one unit and reflected over the y-axis. Using these rules, we can see that the correct choice is B.}

Question 17

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places.
f (x) = 0.2x  - 1.8x - 3.8; g(x) = -0.1x  + 0.8x + 6.7

Accepted Answer

The answer of Find the points of intersection of the...

Question 18

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 19

Use the graph of y = ln x as an aid to sketch the graph of the function.
g(x) = ln(x + 1)

Accepted Answer

The answer of Use the graph of y = ln...

Question 20

Find the absolute extrema of the function on the indicated interval. f (x) = xe^-³^x; [-1, 2]

Accepted Answer

The answer of Find the absolute extrema of the function...

Quiz 6: Inverse Functions

Find the absolute minimum value of the function.

Evaluate the integral.

Find if

Determine f(x) from the table. The values from the table are given to the nearest ten thousandth. 1

Determine whether the function is one-to-one. f (x) =

Use logarithmic differentiation to find the derivative of the function. y = (x + 1)²(8x²- 5)³

Evaluate the integral.

Sketch a graph of the function. f (x) =

Differentiate the function.

If

Find the inverse of the function.

Suppose that g is the inverse of a function F. If f (3) = 4 and f '(3) = 5, find g'0(4) .

Find the integral.

Find an equation of the tangent line to the curve at the given point.

Find f ^-¹(a) for the function f and the real number a. f (x) = x³ + x - 7; a = -5

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. f (x) = 0.2x - 1.8x - 3.8; g(x) = -0.1x + 0.8x + 6.7

Evaluate the integral.

Use the graph of y = ln x as an aid to sketch the graph of the function. g(x) = ln(x + 1)

Find the absolute extrema of the function on the indicated interval. f (x) = xe^-³^x; [-1, 2]

Quiz 6: Inverse Functions

Find the absolute minimum value of the function.

Evaluate the integral.

Find if

Determine f(x) from the table. The values from the table are given to the nearest ten thousandth. 1

Determine whether the function is one-to-one. f (x) =

Use logarithmic differentiation to find the derivative of the function. y = (x + 1)2 (8x2 - 5)3

Evaluate the integral.

Sketch a graph of the function. f (x) =

Differentiate the function.

If

Find the inverse of the function.

Suppose that g is the inverse of a function F. If f (3) = 4 and f '(3) = 5, find g'0(4) .

Find the integral.

Find an equation of the tangent line to the curve at the given point.

Find f -1 (a) for the function f and the real number a. f (x) = x3 + x - 7; a = -5

Find the inverse of F. Then sketch the graphs of f and f -1 on the same set of axes.f (x) = , x ≥\ge≥ 0

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. f (x) = 0.2x - 1.8x - 3.8; g(x) = -0.1x + 0.8x + 6.7

Evaluate the integral.

Use the graph of y = ln x as an aid to sketch the graph of the function. g(x) = ln(x + 1)

Find the absolute extrema of the function on the indicated interval. f (x) = xe-3x; [-1, 2]

Use logarithmic differentiation to find the derivative of the function. y = (x + 1)²(8x²- 5)³

Find f ^-¹(a) for the function f and the real number a. f (x) = x³ + x - 7; a = -5

Find the absolute extrema of the function on the indicated interval. f (x) = xe^-³^x; [-1, 2]