Inverse Functions Test – Precalculus Math (Printable PDF)

Question 1 Domains in Interval Notation (2 points)

Write the domain of each function in interval notation.

1. f(x) = √(2x − 9) (1 point)
2. g(x) = xx² − 16 (1 point)

Question 2 Numerical Compositions (2 points)

Let f(x) = x² + 2x and g(x) = 3x − 4.

1. Find f(g(2)). (1 point)
2. Find g(f(−1)). (1 point)

Question 3 Composite Expressions (2 points)

Let f(x) = x² − 6x and g(x) = x + 3. Simplify (f ∘ g)(x) and (g ∘ f)(x).

Question 4 Domain, Range and Inverse from a Graph (2 points)

The graph of f starts at the closed point (−2, −1) and continues to the right through (7, 2).

1. State the domain and range of f. (1 point)
2. Find f⁻¹(2). (1 point)

Question 5 Find an Inverse Function (3 points)

Determine f⁻¹ for f(x) = 4x + 3x − 2.

Question 6 Verify Inverses (2 points)

Show that f(x) = ∛(x + 5) − 2 and g(x) = (x + 2)³ − 5 are inverse functions.

Question 7 Table of an Inverse (2 points)

The one-to-one function f is given by the table.

1. Complete a table for f⁻¹ with inputs 7, 3, 0 and −4. (1 point)
2. Evaluate f(f⁻¹(−4)) + f⁻¹(7). (1 point)

Question 8 Restrict a Parabola, Then Invert (3 points)

Let f(x) = x² − 6x + 5, shown below.

1. Write f in vertex form. (1 point)
2. Restrict f to x ≥ 3 and find the inverse. (1 point)
3. State the domain and range of the inverse. (1 point)

Question 9 Sale Price with Tax (2 points)

A store takes 20% off the original price p, then adds 7% sales tax to the discounted price.

1. Write the total cost C(p) as one function of p. (1 point)
2. Find the original price when the total is $64.20. (1 point)