Unit 2: Functions
Topic 2.2: Functions, Domain and Range Questions
Practice 20 exam-style questions for IB Math AA SL Topic 2.2. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1State2 marks
2026• Aimnova practice — 2.2.2
State the domain of g(x) = √(x + 1).
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2026• Aimnova practice — 2.2.2
Write down the range of f(x) = x² + 2.
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2026• Aimnova practice — 2.2.3
Given that f(5) = 12, write down f⁻¹(12).
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2026• Aimnova practice — 2.2.3
The graph of f⁻¹ is the reflection of the graph of f in a line. State the equation of that line.
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2026• Aimnova practice — 2.2.1
Given f(x) = 4x − 3, find f(5).
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2026• Aimnova practice — 2.2.2
State the domain of f(x) = 1/(x + 5).
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2026• Aimnova practice — 2.2.1
Given g(x) = x² + 2x, find g(−4).
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2026• Aimnova practice — 2.2.2
State the range of f(x) = (x − 1)² − 4.
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2026• Aimnova practice — 2.2.2
State the range of f(x) = 3ˣ.
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2026• Aimnova practice — 2.2.3
The function f is defined by f(x) = 4x − 1. (a) Find f⁻¹(x). (b) Hence find f⁻¹(7).
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2026• Aimnova practice — 2.2.3
Find the inverse of f(x) = 3x − 6. Give your answer as f⁻¹(x).
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2026• Aimnova practice — 2.2.3
Find the inverse of f(x) = (x − 4)/2.
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2026• Aimnova practice — 2.2.1
Given f(x) = 5 − 2x, solve f(x) = 11.
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2026• Aimnova practice — 2.2.1
For f(x) = 2x − 1, it is given that f(a) = 9. Find the value of a.
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2026• Aimnova practice — 2.2.3
The graph of f passes through (1, 4) and (3, 10). State the two points the graph of f⁻¹ must pass through.
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2026• Aimnova practice — 2.2.2
Find the domain of h(x) = √(2x − 6).
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2026• Aimnova practice — 2.2.3
A function f has domain x ≥ 1 and range y ≤ 5. (a) State the domain of f⁻¹. (b) State the range of f⁻¹.
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2026• Aimnova practice — 2.2.2
The graph of y = f(x) exists only for −3 ≤ x ≤ 4, and its outputs run from −1 up to 8. (a) State the domain. (b) State the range.
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2026• Aimnova practice — 2.2.1
Given f(x) = x² − 7, solve f(x) = 18.
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2026• Aimnova practice — 2.2.1
The function f is defined by f(x) = 3x + 2. (a) Find f(−2). (b) Find the value of x for which f(x) = 17.
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