Unit 2: Functions
Topic 2.5: Composite and Inverse Functions Questions
Practice 19 exam-style questions for IB Math AA SL Topic 2.5. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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2026• Aimnova practice — 2.5.1
f(x) = x² and g(x) = 2x − 1. Find (g∘f)(3).
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2026• Aimnova practice — 2.5.1
f(x) = 3x − 2 and g(x) = x + 4. Find (f∘g)(2).
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2026• Aimnova practice — 2.5.2
Find the inverse of f(x) = 5x − 2, giving your answer as f⁻¹(x).
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2026• Aimnova practice — 2.5.3
The graph of y = f(x) passes through (1, 5) and (5, 2). Find (a) f(1); (b) f⁻¹(2).
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2026• Aimnova practice — 2.5.1
Functions are defined by f(x) = ln x (x > 0) and g(x) = x² + 1. Find an expression for (f∘g)(x).
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2026• Aimnova practice — 2.5.2
Find the inverse of f(x) = (x + 4)/3.
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2026• Aimnova practice — 2.5.2
Find the inverse of f(x) = 3x + 7, and hence find f⁻¹(1).
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2026• Aimnova practice — 2.5.2
Find the inverse of f(x) = (x/2) − 3.
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2026• Aimnova practice — 2.5.2
Show that f⁻¹(x) = (x − 1)/2 is the inverse of f(x) = 2x + 1 by composing the two functions.
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2026• Aimnova practice — 2.5.3
On a graph, f(3) = 1 and f(1) = 4. Find (f∘f)(3).
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2026• Aimnova practice — 2.5.1
f(x) = 4x − 1 and g(x) = x + 2. Solve (f∘g)(x) = 19.
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2026• Aimnova practice — 2.5.3
The graph of f cuts the axes at (0, 4) and (6, 0). Write down where y = f⁻¹(x) cuts the axes.
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2026• Aimnova practice — 2.5.1
f(x) = x + 1 and g(x) = 2x. (a) Find (f∘g)(x). (b) Find (g∘f)(x). (c) State whether they are equal.
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2026• Aimnova practice — 2.5.1
f(x) = 2x + 3 and g(x) = x². Find an expression for (f∘g)(x).
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2026• Aimnova practice — 2.5.1
f(x) = x − 5 and g(x) = x². Find an expression for (g∘f)(x).
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2026• Aimnova practice — 2.5.2
The function f(x) = x² is defined for x ≥ 0. (a) Find f⁻¹(x). (b) State the domain of f⁻¹.
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2026• Aimnova practice — 2.5.2
Find the inverse of f(x) = (2x + 1)/(x − 3).
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2026• Aimnova practice — 2.5.2
A function is defined by f(x) = (5 − 2x)/(x + 1). (a) Find f⁻¹(x). (b) Write down the value f⁻¹ cannot take.
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2026• Aimnova practice — 2.5.1
g(x) = x². Find the linear function f(x) = ax + b such that (f∘g)(x) = 5x² + 1.
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