Inverse Relations and Functions Practice — Grade 11 math

Lesson 6: Inverse Relations and Functions — Practice Questions

1. The graphs of a function and its inverse are symmetric with respect to which line?
- A. the x-axis
- B. the y-axis
- C. the line y = x
- D. the line y = -x
2. If the point (2, 32) is on the graph of f(x) = x^5, then the point (32, ___) must be on the graph of its inverse function.
3. Which of the following functions is the inverse of f(x) = x + 11?
- A. g(x) = x - 11
- B. g(x) = 11 - x
- C. g(x) = 11x
- D. g(x) = x / 11
4. The functions f(x) = x - 15 and g(x) = x + 15 are inverses. If you evaluate f(50), you get 35. What is the value of g(35)? ___
5. A function is defined by the equation y = x^9. Which equation is an equivalent formula for its inverse function?
- A. $x = y^9$
- B. $y = \frac{1}{x^9}$
- C. $x = \frac{1}{y^9}$
- D. y = 9x
6. Let $f(x) = 4x - 5$ and $g(x) = \frac{x+5}{4}$. Find the simplified expression for the composition $f(g(x))$. The result is ___.
7. Let $f(x) = 6x + 2$ and $g(x) = \frac{x-2}{6}$. Find the simplified expression for the composition $g(f(x))$. The result is ___.
8. Which statement correctly describes the necessary condition for two functions, $f(x)$ and $g(x)$, to be inverses?
- A. $f(g(x)) = x$ is sufficient.
- B. $g(f(x)) = x$ is sufficient.
- C. Both $f(g(x)) = x$ and $g(f(x)) = x$ must be true.
- D. $f(x) = -g(x)$ must be true.
9. Consider $f(x) = x+5$ and $g(x) = x-6$. Are these functions inverses of each other?
- A. Yes, because they are both linear functions.
- B. No, because $f(g(x))$ does not simplify to $x$.
- C. Yes, because subtraction is the inverse of addition.
- D. No, because $g(x)$ should be $5-x$.
10. Given $f(x) = x^3 - 1$ and $g(x) = \sqrt[3]{x+1}$. To verify they are inverses, we find $f(g(x))$. What is the resulting expression? $f(g(x)) = $ ___.