Consider the linear function defined by

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

Problem

Consider the linear function

f_{m,b}: \mathbb R \to \mathbb R

defined by

f_{m,b}(x)=mx+b

, where

m,b\in\mathbb R

. (i) State the condition on the parameter

m

that makes

f_{m,b}

one-to-one on

\mathbb R

. (ii) Explain why this condition guarantees the existence of

f_{m,b}^{-1}

and write an explicit formula for the inverse in terms of

m

and

b

. (iii) Describe how the domain and range interchange between

f_{m,b}

and its inverse.