Let be defined by

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let

f:(0,1)\to\mathbb{R}

be defined by

f(x)=\frac{b-x}{1-bx}

, where

b

is a constant such that

0<b<1

. Then, (1)

f

is not invertible on

(0,1)

(2)

f\ne f^{-1}

on

(0,1)

and

f'(b)=\frac{1}{f'(0)}

(3)

f=f^{-1}

on

(0,1)

and

f'(b)=\frac{1}{f'(0)}

(4)

f^{-1}

is differentiable on

(0,1)

Related theory

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