For a fixed real number

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

a\neq -1

, define

f_a: \mathbb R\setminus\{-a\}\longrightarrow \mathbb R, \qquad f_a(x)=\frac{ax+1}{x+a}.

(i) If

f_a(x_1)=f_a(x_2)

for two real numbers

x_1,x_2\neq -a

, obtain the relation between

x_1

and

x_2

. (ii) Hence determine all real values of

a

for which

f_a

is injective on its domain.