Consider the function defined by f(x)= 2x+k x+1

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

Problem

Consider the function

f:\mathbb R\setminus\{-1\}\to\mathbb R\setminus\{k+1\}

defined by

f(x)=\frac{2x+k}{x+1},

where

k

is a real parameter. (a) Determine all real values of

k

for which

f

is one–to–one. (b) Among the values obtained in (a), identify those for which

f

is also onto its codomain, and hence bijective. For each such

k

, write

f^{-1}(x)