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CAIE IGCSE Mathematics Finding Inverse Functions

Practise finding inverse functions by reversing a rule algebraically and using inverse notation to recover inputs or solve for unknown values.

Syllabus
2028–2030
Course
Mathematics 0580
Level
Extended

Exam points

  • write y = f(x), interchange x and y and rearrange fully to state f⁻¹(x)
  • use f⁻¹(a) = b as equivalent to f(b) = a when solving for an unknown value
  • verify an inverse by checking that composition with the original function returns the input

E2.13.2 Understand and find inverse functions f –1(x). question 1

[Maximum number: 2]

10f(x)=4−3x g(x)=x2+x h(x)=3x10 \quad \mathrm{f}(x)=4-3 x \quad \mathrm{~g}(x)=x^{2}+x \quad \mathrm{~h}(x)=3^{x}

Find f−1(x)f^{-1}(x).

f−1(x)=f^{-1}(x)=

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