Mathematics

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