Suppose and there exists a function such that but

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

Problem

Suppose

f:\mathbb R\to\mathbb R

and there exists a function

g:\mathbb R\to\mathbb R

such that

g\circ f=I_{\mathbb R}

but

f\circ g\neq I_{\mathbb R}

. Which of the following can be concluded about

f

? (a)

f

is both injective and surjective (b)

f

is surjective but not injective (c)

f

is injective but not surjective (d)

f

is neither injective nor surjective