Unit 2: Functions
Topic 2.7: Inverse and Composite Functions Questions
Practice 20 exam-style questions for IB Math AI SL Topic 2.7. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
f(x) = x + 4, g(x) = 2x. Then (f∘g)(3) equals:
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2026
The point (2, 7) lies on y = f(x). Which point must lie on y = f⁻¹(x)?
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2026
For most pairs of functions, (f∘g)(x) and (g∘f)(x) are:
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2026
Sketch the point on the graph of that corresponds to it.
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2026
Given f(x) = 4x − 1 and g(x) = 2 − x, find (f∘g)(3).
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The temperature of a metal block after x minutes is given by feeding time into g(x) = 0.5x and then into f(t) = . Find the temperature after 4 minutes, giving the answer to 3 significant figures.
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2026
A price is taxed by t(x) = 1.2x and reduced by a \$10 coupon c(x) = x − 10. On a \$100 item, which is cheaper for the customer: tax-then-coupon, or coupon-then-tax?
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The cost of printing x flyers is C(x) = 0.2x + 15 dollars. Find C⁻¹(35) and interpret it.
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2026
f(x) = √x and g(x) = x − 9. The domain of (f∘g)(x) is:
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Functions are given in a table: g(0) = 3, g(1) = 0, g(3) = 5 and f(0) = 2, f(3) = 4, f(5) = 1. Find (f∘g)(0) and (f∘g)(1).
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2026
Why must the domain of f(x) = x² be restricted before taking an inverse?
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f(x) = x² + 2 and g(x) = 3x. Find an expression for (g∘f)(x).
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2026
For f(x) = 2x − 1, find the x-coordinate where f(x) = f⁻¹(x).
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2026
For f(x) = 3x + 1, the inverse f⁻¹(x) equals:
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2026
f(x) = x² − 4 for x ≥ 0. Find f⁻¹(x) and state its domain.
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A cooling cup of coffee has temperature f(x) = 20 + °C after x minutes. Find f⁻¹(50), giving your answer to the nearest minute, and interpret it.
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