Which statement best describes the domain of f(x)?

The domain of f(x) is the same as the domain of both g(x) and h(x).

The domain of f(x) is the same as the range of both g(x) and h(x).

The domain of f(x) contains all the real numbers greater than zero.

The domain of f(x) contains all the real numbers less than zero.

If a given function f(x) has an inverse function, which of the following statements is true?

If f(x) has a y-intercept at (0, c), then the x-intercept of the inverse must be (c, 0).

If (a, b) is on the graph of f(x), then the graph of the inverse must contain (-b, -a).

Both f(x) and its inverse must have the same domain.

Both f(x) and its inverse must have the same y-intercept.

A quadratic function has its vertex at (4, –4), x-intercepts (2, 0) and (6, 0), and a y-intercept of (0, 12). Which table best represents the square root function that is the inverse of this quadratic function?

B. x | y 0 | 6 4 | -4 12 | 0 32 | 4

A. x | y 0 | 12 2 | 0 4 | -4 6 | 0

C. x | y -4 | 4 0 | 2 12 | 0 32 | -2

D. x | y 0 | -12 2 | 0 4 | 4 6 | 0

Cristian purchases a car for $10,000 that he will use to go back and forth between his home and community college. The graph shows the depreciating value of his car over time in years. What is the range of the inverse of the function shown in the graph? Write the range of the inverse in set builder notation and explain how its range relates to depreciation and time.

The range is the set of all possible values of time.

The range is the set of all possible values of car value.

The range is the set of all possible values of depreciation rate.

The range is the set of all possible values of years.

Determine whether or not the functions shown in the graph are inverse functions.

No, they are not inverse functions.

Yes, they are inverse functions.

Are f(x) and g(x) inverses? Why or why not?

Yes, because f(g(x)) = x and g(f(x)) = x

No, because f(g(x)) ≠ x or g(f(x)) ≠ x

No, because they have different domains

Which of the following tables represents an inverse of the function shown in the graph if the graphed function’s domain is restricted to all real numbers less than or equal to five?

Table B: (1, 5), (2, 4), (3, 3), (4, 2)

Table A: (5, 1), (4, 2), (3, 3), (2, 4)

Table C: (5, 5), (4, 4), (3, 3), (2, 2)

Table D: (1, 1), (2, 2), (3, 3), (4, 4)

What is the square root function that is the inverse of f(x) = 4(x + 7)² and its restricted domain of (-∞, -7]?

g(x) = - $$\sqrt[]{\frac{x}{4}}-7$$

g(x) = $$\sqrt[]{\frac{x}{4}}-7$$

g(x) = $$-\sqrt{\frac{x}{4}}+7$$

g(x) = $$\sqrt{\frac{x}{4}}+7$$

Determine if f(x) = (x + 5)³ and $$g(x)=^3\sqrt{x}-5$$ represent a function and its inverse. Choose the correct explanation.

Yes, because f(g(x)) = x and g(f(x)) = x.

No, because g(x) is not the inverse of f(x).

What is the inverse of the function f(x) = 64(x + 2)³ - 8?

f⁻¹(x) = $$\sqrt[3]{\frac{x-8}{64}}-2$$

f⁻¹(x) = $$\frac{\sqrt[3]{x+8}}{64}-2$$

f⁻¹(x) = $$\sqrt[3]{\frac{x+8}{64}}-2$$

f⁻¹(x) = $$\frac{\sqrt[3]{x-8}}{64}+2$$

Compare and contrast the domain, range, and intercepts of cubic and cube root functions that are inverses.

Cubic functions and cube root functions both have a domain and range of all real numbers and intercepts at the origin.

Cubic functions have a domain and range of all real numbers, while cube root functions have a domain and range of non-negative real numbers.

Cubic functions have a domain and range of all real numbers, while cube root functions have a domain and range of all real numbers.

Cubic functions have intercepts at the origin, while cube root functions have no intercepts.

What attributes such as domain, range, intercept(s), maximum or minimum values do the inverses of the three functions shown in the graph below have in common?

They all have the same intercept(s).

They all have the same maximum or minimum values.

Compare and contrast the domain and range of the functions. p(x) = 0.5(2x – 7) + 3 q(x) = 0.5(2x – 7)² + 3 $$r(x)=0.5(2)^{\left(2x-7\right)}+3$$

The range of p(x) is all real numbers, q(x) has a range of y ≥ 3, and r(x) has a range of y > 3.

The domain of p(x) and q(x) is all real numbers, while r(x) has a domain of x > 7.

All functions have the same domain and range.

The domain of q(x) is restricted, while p(x) and r(x) have unrestricted domains.

What are the x-intercept and y-intercept of the original function and its inverse, and is the inverse also a function?

The x-intercept of the original function is at (a, 0), the y-intercept is at (0, b), the x-intercept of the inverse is at (b, 0), the y-intercept is at (0, a), and the inverse is a function.

The x-intercept of the original function is at (e, 0), the y-intercept is at (0, f), the x-intercept of the inverse is at (g, 0), the y-intercept is at (0, h), and the inverse is not a function.

The x-intercept of the original function is at (i, 0), the y-intercept is at (0, j), the x-intercept of the inverse is at (k, 0), the y-intercept is at (0, l), and the inverse is a function.

The x-intercept of the original function is at (m, 0), the y-intercept is at (0, n), the x-intercept of the inverse is at (o, 0), the y-intercept is at (0, p), and the inverse is not a function.

Are f(x) and g(x) inverses? Choose the correct explanation.

Yes, because f(g(x)) = x and g(f(x)) = x.

No, because f(g(x)) ≠ x and g(f(x)) ≠ x.

No, because f(x) and g(x) have different domains.

Chapter 3 review Inverse Functions

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Chapter 3 review Inverse Functions

Quiz

•

Mathematics

•

12th Grade

•

Practice Problem

•

Hard

Charlotte Brewer

Used 10+ times

FREE Resource

36 questions

Show all answers

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If a given function f(x) has an inverse function f⁻¹(x), which of the following statements is true?

If (a, b) is on the graph of f(x), then the graph of f⁻¹(x) must contain (−a, −b).

If (a, b) is on the graph of f(x), then the graph of f⁻¹(x) must contain (−b, −a).

If f(x) has an x-intercept at (c, 0), then the x-intercept of f⁻¹(x) must be (c, 0).

If f(x) has an x-intercept at (c, 0), then the y-intercept of f⁻¹(x) must be (0, c).

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The table below contains values of the function f(x). Which of the following tables represents f⁻¹(x)?

Table A

Table B

Table C

Table D

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The domain of f(x) must be restricted to {x | x ≥ 0}.

The domain of f(x) must be restricted to {x | x ≤ 0}.

The domain of f(x) must be restricted to {x | x ≥ -2}.

The domain of f(x) must be restricted to {x | x ≤ -2}.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

(-∞, d)

(d, ∞)

(-∞, ∞)

The domain of the inverse cannot be determined.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If the graph represents an exponential function, what is the equation of the vertical asymptote of its inverse logarithmic function?

x = 0

x = -2

y = 0

y = -2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What point do all three functions represented in the tables below have in common?

maximum value

minimum value

x-intercept

y-intercept

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