Mathematics

Problem

Let

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

be given by

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

. a. (i) Determine a function

g

such that

(g\circ f)(x)=x

for all

x\ne1

. b. (ii) Verify that

(f\circ g)(y)=y

for all admissible values of

y