Let be bijective and let be a function that is not one–one

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

Problem

Let

f:\mathbb R\to\mathbb R

be bijective and let

g:\mathbb R\to\mathbb R

be a function that is not one–one. Which one of the following statements is necessarily true? (a)

g\circ f

is invertible (b) Neither

f\circ g

nor

g\circ f

is invertible (c)

f\circ g

is invertible (d) Both

f\circ g

and

g\circ f

are invertible