2025 IGCSE 0580 May/June P21 Q14

2025 IGCSE 0580 May/June P21 Q14

8 marks

\(\mathrm{f}(x)=3x-4\qquad\mathrm{g}(x)=4x+1\)

  1. Find \(\mathrm{f}(-2)\).[1]
  2. Find \(\mathrm{f}^{-1}(x)\).[2]
  3. \(\mathrm{fg}(x)=ax+b\)
    Find the value of \(a\), and the value of \(b\).[2]
  4. Simplify.
    \(\dfrac{2}{\mathrm{f}(x)}-\dfrac{5}{\mathrm{g}(x)}\)
    Give your answer as a single fraction in terms of \(x\).[3]

Solution:

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Answer:(a) \(-10\). (b) \(\dfrac{x+4}{3}\). (c) \(a=12,\ b=-1\). (d) \(\dfrac{22-7x}{(3x-4)(4x+1)}\).

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