AQA · Mathematics · 8300
GCSE Maths: Composite functions
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise for Composite functions (Corbettmaths Video 370), 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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Given f(x) = 3x + 5, what is f(−2)?
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−1. Substitute x = −2: 3(−2) + 5 = −6 + 5 = −1.
Given f(x) = 3x − 8, solve f(x) = 7.
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x = 5. Set 3x − 8 = 7, so 3x = 15 and x = 5.
What does the composite function fg(x) mean?
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f(g(x)) — apply g first, then apply f to the result. The function nearest x is applied first.
Given f(x) = x + 5 and g(x) = 3x − 1, what is fg(1)?
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7. First g(1) = 3(1) − 1 = 2, then f(2) = 2 + 5 = 7.
Given f(x) = 2x + 1 and g(x) = x − 5, find gf(x).
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gf(x) = 2x − 4. Substitute f(x) into g: (2x + 1) − 5 = 2x − 4.
How do you find the inverse function f⁻¹(x)?
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Write y = f(x), swap x and y, then rearrange to make y the subject. The result is f⁻¹(x).
Given f(x) = 5x + 1, what is f⁻¹(x)?
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f⁻¹(x) = (x − 1) / 5. From y = 5x + 1, swap to x = 5y + 1 and rearrange: y = (x − 1)/5.
Given f(x) = 2x − 3, what is f⁻¹(7)?
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5. f⁻¹(x) = (x + 3)/2, so f⁻¹(7) = 10/2 = 5. Equivalently, solve 2x − 3 = 7.
The notation f⁻¹(x) denotes the ? function of f, which reverses the effect of f.
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inverse
Given f(x) = x² + 4x − 1, express f(2x) in the form ax² + bx + c.
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4x² + 8x − 1. Replace every x with 2x: (2x)² + 4(2x) − 1.
Given f(x) = kx + 7, g(x) = 3x − 2 and gf(1) = 34, find k.
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k = 5. f(1) = k + 7, so g(k + 7) = 3(k + 7) − 2 = 3k + 19 = 34, giving k = 5.
Given f(x) = x² + 3x + 8, simplify f(x + 1) − f(x).
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2x + 4. f(x + 1) = x² + 5x + 12; subtracting x² + 3x + 8 leaves 2x + 4.
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