Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for an inverse functions quiz? Then this Algebra 2 quiz on Combining and Inverting Functions asks 10 multiple-choice questions with instant feedback.
Ten multiple-choice questions on operations with functions, composition, and inverse functions. Compose from the inside out and check the order, since h(k(x)) usually differs from k(h(x)).
Standards: F-BF.A.1b, F-BF.A.1c, F-BF.B.4a · Level: Grade 11 Algebra 2
What this Combining and Inverting Functions quiz checks
- (f + g)(x), (f − g)(x), and (f · g)(x) combine the outputs of f and g.
- Composition f(g(x)) works inside-out and is not usually commutative.
- Find an inverse by swapping x and y and solving for y.
- Inverses satisfy f(f−1(x)) = x and f−1(f(x)) = x.
- The graphs of f and f−1 are mirror images across the line y = x.
The 10 questions of the quiz
- If h(x) = x + 3 and k(x) = 2x, what is h(k(x))?
- If h(x) = 7x and k(x) = x2, what is (h − k)(x)?
- What is the inverse of h(x) = x − 13?
- What is the inverse of h(x) = 4x + 12?
- The graph of h contains the point (1, 5). Which point must be on the graph of h−1?
- What does h(h−1(x)) equal?
- Let h(x) = √x and k(x) = x + 9. What is the domain of h(k(x))?
- The graph of h−1 is a reflection of the graph of h across which line?
- Why does this graph have no inverse function over all real numbers?
- If k(x) = x2 + 4 and h(x) = 5x, what is h(k(3))?
After the quiz
Missed a question? Reread the Combining and Inverting Functions lesson, then take the quiz again. Next, solve the Algebra 2 worksheet on Combining and Inverting Functions, one star first, then two and three stars. Finally, take the chapter test under real conditions, without notes and with a timer.
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