Question 1

Which of the following statements best describes an inverse function $$f^{-1}(x$$)$$?

Accepted Answer

It reverses the domain and range of $$f(x).$$

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

What is the horizontal line test used for?

Accepted Answer

To determine if a function is one-to-one.

Question 6

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

Accepted Answer

$$(-\infty, 1) \cup (1, \infty)$$

Question 7

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 8

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

Accepted Answer

Replace $$f(x)$$ with $$y$$, swap $$x$$ and $$y$$, solve for $$y$$, replace $$y$$ with $$f^{-1}(x$$)$$

Question 9

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

Accepted Answer

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

Question 10

A function $$f(x) is $$one-to-one if:

Accepted Answer

Each $$y$$ value corresponds to exactly one $$x$$ value.

Question 11

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

Accepted Answer

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

Question 12

Which of the following is true about the graph of a function and its inverse?

Accepted Answer

They are symmetric across the line $$y = x$$

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

Question 15

If $$f(x) = 2x + 3$$ and $$f^{-1}(x$$) = \frac{x-3}{2}$$, what is f(f$$^{-1}$$(5))$$?

Accepted Answer

$$5$$

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

Question 19

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

Accepted Answer

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

Inverse Functions and Their Representations

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