Question 1

Which of the following statements best describes the relationship between a function $$f$$ and its inverse $$f^{-1}$$?

Accepted Answer

The domain of $$f is $$the range of $$f^{-1}$$, and the range of $$f is $$the domain of $$f^{-1}.$$

Question 2

Given $$f(x) = 2x + 1$$, what is $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-1}{2}$$

Question 3

If $$f(x) = 3x - 2$$, what is the domain and range of $$f^{-1}(x$$)$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, \infty)$$

Question 4

Which of the following functions is NOT one-to-one?

Accepted Answer

$$f(x) = x^2$

Question 5

A function $$f is $$one-to-one if:

Accepted Answer

Every horizontal line intersects the graph of $$f at $$most once.

Question 6

If $$f(x) = \frac{x+2}{x-1}$$, what is $$f^{-1}(x$$)$$?

Accepted Answer

Question 7

Given $$f(x) = \frac{2x-1}{3}$$, what is $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{3x+1}{2}$$

Question 8

If $$f(x)$$ has a vertical asymptote at $$x = a$$, what does $$f^{-1}(x$$)$$ have?

Accepted Answer

A horizontal asymptote at $$y = a$$

Question 9

If $$f(x) = x^3$, what is f$$^{-1}$$(x)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x}$$

Question 10

Which of the following is the correct process to find the inverse of a function $$f(x)$$?

Accepted Answer

Replace $$f(x)$$ with $$y$$, solve for $$x$$, then replace $$x$$ with $$y$$

Question 11

If $$f(x) = \frac{1}{x}$$, what is the domain and range of $$f^{-1}(x$$)$$?

Accepted Answer

Domain: $$(-\infty, 0) \cup (0, \infty)$$, Range: $$(-\infty, 0) \cup (0, \infty)$$

Question 12

If $$f(x) = x^2$ for x$$ \geq 0$$, what is f$$^{-1}$$(x)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt{x}$$

Question 13

Which of the following is a real-world example of an inverse function?

Accepted Answer

Converting Celsius to Fahrenheit and vice versa

Question 14

If $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f^{-1}(x$$)$$?

Accepted Answer

Domain: $$(-\infty, 0) \cup (0, \infty)$$

Question 15

If $$f(x) = 2x + 1$$, what is $$f^{-1}(5$$)$$?

Accepted Answer

$$f^{-1}(5) = 2$

Question 16

If $$f(x) = x^2$ for x$$ \geq 0$$, what is the range of f$$^{-1}$$(x)$$?

Accepted Answer

Range: $$[0, \infty)$$

Question 17

If the graph of $$f(x) is $$symmetric across the line $$y = x$$, what can be said about $$f(x)$$ and $$f^{-1}(x$$)$$?

Accepted Answer

They are inverses of each other.

Question 18

If $$f(x) = \frac{x-1}{x+2}$$, what is the domain of $$f(x)$$?

Accepted Answer

Domain: $$(-\infty, -2) \cup (-2, \infty)$$

Inverse Functions and Their Representations

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