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Composite and inverse functionsAQA A-Level Maths: Flashcards

What these 13 flashcards ask

  • What does fg(x) mean?
  • Is fg(x)=gf(x) in general?
  • If f(x)=3x-2, g(x)=x^2+1, find fg(x).
  • What is the domain of fg?
  • What does f^{-1} do?
  • When does f^{-1} exist?
  • Method for finding f^{-1}(x)?
  • Domain of f^{-1} in terms of f?
  • Range of f^{-1} in terms of f?
  • How is the graph of y=f^{-1}(x) related to y=f(x)?
  • Simplify ff^{-1}(x).
  • If f(x)=(x-2)^2+3 for x\ge2, what is f^{-1}(x)?
  • For an increasing function, where do the graphs of f and f^{-1} meet?

Exam questions on Composite and inverse functions

  1. The functions ff and gg are defined for all real xx by f(x)=3x−2f(x)=3x-2 and g(x)=x2+1g(x)=x^2+1.
    Solve fg(x)=13fg(x)=13.2 marks
  2. The function hh is defined by h(x)=2x+1x−3h(x)=\dfrac{2x+1}{x-3} for x∈Rx\in\mathbb{R}, x≠3x\neq3.
    Given that h−1(a)=5h^{-1}(a)=5, find the value of aa without finding h−1(x)h^{-1}(x).2 marks
  3. The function ff is defined by f(x)=(x−2)2+3f(x)=(x-2)^2+3 for x≥2x\ge2.
    State the range of ff and find f−1(x)f^{-1}(x).3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).