Let be given by .

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

Problem

Let

f:\mathbb R\setminus\{1\}\to\mathbb R\setminus\{2\}

be given by

f(x)=\dfrac{2x+3}{x-1}

. (i) Determine a function

g

such that

(g\circ f)(x)=x

for all

x\ne1

. (ii) Verify that

(f\circ g)(y)=y

for all admissible values of

y

.

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