Inverse functions and their graphsEdexcel International A Level Maths: Flashcards

What these 13 flashcards ask

What does an inverse function do?
What must be true for f^{-1} to exist?
How do you restrict a domain to get an inverse?
State the identity for inverse functions.
Steps to find f^{-1}?
Domain of f^{-1}?
Range of f^{-1}?
How is the graph of f^{-1} related to the graph of f?
If (a,b) is on y=f(x), which point is on y=f^{-1}(x)?
Find f^{-1} for f(x)=3x-4.
Find the inverse of f(x)=x^2, x\geqslant0.
What is a self-inverse function?
If f is increasing, how can f(x)=f^{-1}(x) be solved?

Exam questions on Inverse functions and their graphs

The function $f$ is defined by $f(x)=\dfrac{2x+1}{x-3}$ , $x\in\mathbb{R}$ , $x\neq3$ .
Find the value of $f^{-1}(5)$ .2 marks
The function $g$ is defined by $g(x)=x^2-6x+5$ , $x\geqslant3$ .
Explain why $g$ has an inverse function with the domain $x\geqslant3$ , but would not have one if the domain were $x\in\mathbb{R}$ .2 marks
The function $f$ is defined by $f(x)=2\mathrm{e}^{x}-5$ , $x\in\mathbb{R}$ .
Find $f^{-1}(x)$ and state its domain.3 marks

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).