Mapping/Composition/Leftinjective/Exercise

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

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

be mappings 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.

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