Question 1

Given $$f(x) = \frac{x-2}{5}$$ and $$f^{-1}(x) = 5x + 2$, use composition to determine if these functions are inverses of each other. What is f(f$$^{-1}$$(x))$$?

Accepted Answer

$$x$$

Question 2

Given $$f(x) = \frac{x-2}{5}$$ and $$f^{-1}(x) = 5x + 2$, use composition to determine if these functions are inverses of each other. What is f$$^{-1}$$(f(x))$$?

Accepted Answer

$$x$$

Question 3

Suppose $$f(x) = 2\sqrt{x+3} - 2$$ and $$f^{-1}(x$$) = \left(\frac{x+2}{2}\$$right)^2 - 3$. What is f(f$$^{-1}$$(x))$$?

Accepted Answer

$$x$$

Question 4

Suppose $$f(x) = 2\sqrt{x+3} - 2$$ and $$f^{-1}(x$$) = \left(\frac{x+2}{2}\$$right)^2 - 3$. What is f$$^{-1}$$(f(x))$$?

Accepted Answer

$$x$$

Question 5

If $$f(x) = \frac{x-2}{5}$$ and $$g(x) = 5x + 2$$, which of the following statements is true?

Accepted Answer

$$f$$ and $$g$$ are inverses of each other because $$f(g(x)) = x$$ and $$g(f(x)) = x$$

Question 6

Which of the following is the correct process to verify if two functions are inverses using composition?

Accepted Answer

Compute both $$f(g(x))$$ and $$g(f(x))$$ and check if both equal $$x$$

Question 7

Given $$f(x) = 2\sqrt{x+3} - 2$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \geq -3$$

Question 8

Given $$f^{-1}(x$$) = \left(\frac{x+2}{2}\$$right)^2 - 3$, what is the range of f$$^{-1}$$(x)$$?

Accepted Answer

$$y \geq -3$$

Question 9

If $$f(x) = \frac{x-2}{5}$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$5x + 2$$

Question 10

If $$f(x) = 2\sqrt{x+3} - 2$$, what is the correct formula for $$f^{-1}(x$$)$$?

Accepted Answer

$$\left(\frac{x+2}{2}\$$right)^2$$ - 3$$

Question 11

A real-world scenario: A temperature in Celsius is converted to Fahrenheit by $$f(x) = \frac{9}{5}x + 32. $$What is the inverse function to convert Fahrenheit back to Celsius?

Accepted Answer

$$f^{-1}(x$$) = \frac{5}{9}(x-32)$$

Using Composition to Test If Two Functions Are Inverses

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