Mapping/Composition/Leftinjective/Exercise

Let ${}L,M,N$ be sets and let

$f:L\longrightarrow M{\text{ and }}g:M\longrightarrow N$

be functions with their composition

$g\circ f\colon L\longrightarrow N,x\longmapsto g(f(x)).$

Show that if ${}g\circ f$ is injective,

then also ${}f$ is injective.

To solution