Practice finding inverse functions, evaluating compositions, and using composition to verify that two functions are inverses.
Read each problem carefully. Show your work in the space provided and write final answers clearly.
Finding inverses and evaluating composed functions
Math - Grade 9-12
- 1
Let f(x) = 3x - 7 and g(x) = x + 5. Find (f composed with g)(x), written as f(g(x)).
- 2
Let f(x) = x squared + 2 and g(x) = 4x. Find g(f(x)).
- 3
Let f(x) = 2x + 1 and g(x) = x squared - 3. Find f(g(4)).
- 4
Find the inverse of f(x) = x - 9.
- 5
Find the inverse of f(x) = 5x + 2.
- 6
Find the inverse of f(x) = (x - 4)/3.
- 7
Use composition to verify that f(x) = 2x - 6 and g(x) = (x + 6)/2 are inverse functions.
- 8
Let f(x) = x cubed. Find f^-1(x).
- 9
Let f(x) = square root of (x + 1). State the domain of f and find f^-1(x).
- 10
Let f(x) = x squared with domain x greater than or equal to 0. Find f^-1(x).
- 11
Let f(x) = 1/(x - 2). Find f^-1(x).
- 12
Let f(x) = 4x - 1 and g(x) = (x + 1)/4. A student says f(g(x)) = x but g(f(x)) = 4x, so the functions are not inverses. Find the error and give the correct result.