Inverse Functions Test – Algebra 2 Math (Printable PDF)

Question 1 Combining functions (2 points)

For h(x) = x² − 3x and k(x) = 2x + 7, find (h + k)(x) (1 point) and (h · k)(−2) (1 point).

Question 2 Composition (3 points)

For h(x) = 3x − 2 and k(x) = x² + 1, find h(k(x)) (1 point), k(h(x)) (1 point), and h(k(2)) (1 point).

Question 3 Find an inverse (3 points)

Find the inverse of h(x) = 3x − 85 (2 points) and verify one of the two compositions (1 point).

Question 4 Inverse from a graph (3 points)

The graph of a linear function h is shown with the dashed line y = x and the points (0, 1), (2, 2), and (4, 3).

1. List three points on the graph of h⁻¹. (1 point)
2. Write the equation of h⁻¹. (1 point)
3. Which point is on both graphs? (1 point)

Question 5 Restricted domain (3 points)

The function h(x) = x² + 5 is defined only for x ≥ 0. The graph is shown.

1. Find h⁻¹(x). (2 points)
2. State the domain and the range of h⁻¹. (1 point)

Question 6 Domain of a composition (2 points)

For h(x) = √(x − 7) and k(x) = x², find h(k(x)) (1 point) and k(h(x)) (1 point), and state the domain of each.

Question 7 Sale and coupon (2 points)

A cart costs $48. A 25%−off sale is S(p) = 0.75p and an $8 coupon is K(p) = p − 8. Find the price when the sale is applied first and when the coupon is applied first. Which order is cheaper?

Question 8 Verify inverses (2 points)

Show by composition that h(x) = x³ − 1 and k(x) = ∛(x + 1) are inverses.