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Composite and inverse functionsEdexcel A-Level Maths: Flashcards

What these 13 flashcards ask

  • What does fg(x) mean?
  • What is the condition for f^{-1} to exist?
  • State the identities linking f and f^{-1}.
  • How is the domain of f^{-1} related to f?
  • How are the graphs of y=f(x) and y=f^{-1}(x) related?
  • What is a many-one function? Give an example.
  • Why is y^2=x not a function?
  • Steps to find f^{-1}(x)?
  • For f(x)=3x-2, g(x)=x^2+1: find fg(x).
  • For the same f and g: find gf(x).
  • Range of f(x)=x^2-4x+7, x\geq2?
  • When is fg defined?
  • If (2,7) lies on y=f(x), which point lies on y=f^{-1}(x)?

Exam questions on Composite and inverse functions

  1. The functions ff and gg are defined by f(x)=3x−2f(x)=3x-2, x∈Rx\in\mathbb{R}, and g(x)=x2+1g(x)=x^2+1, x∈Rx\in\mathbb{R}.
    Solve the equation fg(x)=49fg(x)=49.2 marks
  2. The function hh is defined by h(x)=2x+1x−3h(x)=\frac{2x+1}{x-3}, x∈Rx\in\mathbb{R}, x≠3x\neq3.
    Find the value of h−1(5)h^{-1}(5).2 marks
  3. The function ff is defined by f(x)=x2−4x+7f(x)=x^2-4x+7, x≥2x\geq2.
    Express f(x)f(x) in the form (x−a)2+b(x-a)^2+b and hence state the range of ff.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).