# Math Help - proof about composition

Let f : A to B and g : B to C.
if g o f is surjective then g must be surjective

how do you prove this

Let f : A to B and g : B to C.
if g o f is surjective then g must be surjective

how do you prove this

Let $c\in C$ : since $g\circ f$ is surjective there exists a $a\in A\,\,s.t.\,\,\,g\circ f(a)=c\Longrightarrow$ denote $b=f(a)\in B\Longrightarrow g(b)=g(f(a))=c\Longrightarrow g$ is surjective.

Tonio

3. Originally Posted by tonio
Let $c\in C$ : since $g\circ f$ is surjective there exists a $a\in A\,\,s.t.\,\,\,g\circ f(a)=c\Longrightarrow$ denote $b=f(a)\in B\Longrightarrow g(b)=g(f(a))=c\Longrightarrow g$ is surjective.

Tonio
can you elaborate a little more on this