Edexcel A-Level Mathematics A2 P3.1.2 Definition of a Function Questions

Practise using function notation, domains, ranges, inverses and composites to solve for values, equations and transformed graph features.

Exam points

find f^-1(x) by rearranging y=f(x), then state the correct domain or range restriction
use endpoints or asymptotes to state the range of a function on its given domain

[Maximum number: 3]

The function f is defined by

f(x)=\frac{5x}{x^2+7x+12}+\frac{5x}{x+4},\qquad x>0

Find $f^{-1}$ .

\begin{aligned}y&=\frac{5x}{x+3}\\xy+3y&=5x\\5x-xy&=3y\\x&=\frac{3y}{5-y}.\end{aligned}

f^{-1}(x)=\frac{3x}{5-x}

Domain: 0<x<5.

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