AQA · Mathematics · 8300
GCSE Maths: Inverse functions
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise for Inverse functions (Corbettmaths Video 369), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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In the composite function fg(x), which function is applied first?
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g — fg(x) means f(g(x)), so g is applied first and f is applied to the result.
What does the notation ff(x) mean?
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Apply f twice: ff(x) = f(f(x)).
Given f(x) = 3x + 5, what is f(−2)?
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−1, since 3 × (−2) + 5 = −6 + 5.
Given f(x) = 3x − 8, solve f(x) = 7.
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x = 5, since 3x − 8 = 7 gives 3x = 15.
Given f(x) = x + 5 and g(x) = 3x − 1, what is fg(1)?
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7 — g(1) = 2, then f(2) = 7.
Given f(x) = 2x + 1 and g(x) = x − 5, find fg(x).
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fg(x) = 2x − 9 — substitute g(x) into f: 2(x − 5) + 1.
What does the notation f⁻¹(x) denote?
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The inverse function of f — it reverses f, so f⁻¹(f(x)) = x.
What is the method for finding the inverse of a function f(x)?
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Write y = f(x), swap x and y, then rearrange to make y the subject.
Given f(x) = 2x − 3, find f⁻¹(x).
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f⁻¹(x) = (x + 3) / 2 — reverse the steps: add 3, then divide by 2.
Given f(x) = x² + 4x − 1, express f(x + 2) in the form ax² + bx + c.
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x² + 8x + 11 — expand (x + 2)² + 4(x + 2) − 1.
Given f(x) = 5x + 7 and g(x) = 3x − 18, find a such that f(a) = g(a).
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a = −12.5 — 5a + 7 = 3a − 18 gives 2a = −25.
Given f(x) = x² + 3x + 8, what is f(x + 1) − f(x)?
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2x + 4 — the x² and constant terms cancel, leaving (2x + 1) + 3.
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