2.7 Composite and inverse functionsIB Maths: Applications and Interpretation HL: Flashcards

What these 13 flashcards ask

What does (f\circ g)(x) mean?
Is f\circ g=g\circ f in general?
If f(x)=2x+3 and g(x)=x^2, what is (f\circ g)(x)?
If f(x)=2x+3 and g(x)=x^2, what is (g\circ f)(x)?
What does f^{-1} do?
What condition must f meet to have an inverse?
How do you find f^{-1}(x)?
What is (f\circ f^{-1})(x)?
What is (f^{-1}\circ f)(x)?
How are the domain and range of f and f^{-1} related?
Is f^{-1}(x)=\frac{1}{f(x)}?
How can f(x)=(x-3)^2-2 be given an inverse?
Inverse of f(x)=(x-3)^2-2 for x\geq3?

Exam questions on 2.7 Composite and inverse functions

$f(x)=2x+3$ and $g(x)=x^2$ , for $x\in\mathbb{R}$ .
Solve $(f\circ g)(x)=11$ .2 marks
The fare in EUR for a taxi journey of $d$ km is $f(d)=3+1.2d$ , for $d\geq0$ . Fares are converted to AED using $g(x)=4x$ .
A passenger is charged 96 AED. Find the distance of the journey.2 marks
$f(x)=(x-3)^2-2$ , defined for $x\in\mathbb{R}$ .
(i) Explain why $f$ has no inverse function on the given domain. (ii) State the largest domain of the form $x\geq k$ on which $f$ has an inverse, and the range of $f$ on this 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).