Mathematics

Mathematics

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

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