Let be given by and by

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

Problem

Let

f:\mathbb R\to\mathbb R

be given by

f(x)=2x+3

and

g:\mathbb R\to\mathbb R

g(x)=\dfrac{x-3}{2}

. Which of the following statements is true? (a)

g\circ f=x

but

f\circ g\neq x

, so

f

and

g

are not mutual inverses (b) Both

f\circ g

and

g\circ f

equal

x

, so

f

and

g

are mutual inverses (c)

f\circ g=x

but

g\circ f\neq x

, so

f

and

g

are not mutual inverses (d) Both

f\circ g

and

g\circ f

simplify to

2x

, so

f

and

g

are not mutual inverses