A Level

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Define

h:\mathbb R\setminus\{-2\}\to \mathbb R\setminus\{1\}

h(x)=\dfrac{x}{x+2}

. (i) For an arbitrary

y

in the codomain, solve

h(x)=y

for

x

. (ii) Verify that the solution obtained in (i) never equals

x=-2

and identify any extraneous roots, if present. (iii) Hence prove that

h

is surjective onto its codomain

\mathbb R\setminus\{1\}