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A2 Unit 3 Pure Mathematics B

Quick questions on Functions: modulus, composite, inverse and partial fractions - WJEC A-Level Maths

7short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is the modulus function?
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The modulus (or absolute value) ∣x∣|x| equals xx when x≥0x \ge 0 and −x-x when x<0x < 0, so it is never negative.
What are composite functions?
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A composite function applies one function then another. The notation fg(x)fg(x) means "do gg first, then ff": fg(x)=f(g(x))fg(x) = f(g(x)).
What are inverse functions?
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The inverse f−1f^{-1} undoes ff, so f−1(f(x))=xf^{-1}(f(x)) = x. It exists only if ff is one-to-one (each output comes from exactly one input).
What are partial fractions?
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A proper rational expression (degree of numerator below degree of denominator) splits into a sum with one fraction per factor of the denominator.
What is q1?
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Solve ∣x−2∣=6|x - 2| = 6. [2 marks]
What is q2?
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Given f(x)=x2f(x) = x^2 and g(x)=x+1g(x) = x + 1, find fg(x)fg(x). [2 marks]
What is q3?
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Find the inverse of f(x)=1x−2f(x) = \dfrac{1}{x - 2}, x≠2x \neq 2. [3 marks]

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