Consider the function defined by

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

Problem

Consider the function

f: \mathbb R \to \mathbb R

defined by

f(x)=ax+b

, where

a\neq 0

. (i) State the necessary and sufficient condition for a real-valued function to possess an inverse function. (ii) Prove that the given function

f

is both injective and surjective. (iii) Hence obtain an explicit expression for

f^{-1}(x)

and clearly mention its domain and range.