$\forall$ functions $f,g,h$ if $f \circ h = g \circ h$ and $h$ is onto, then $f=g$ .
I think this statement is true, as I draw diagrams for myself. However I have trouble proving it so I don't know if it's really a true statement. Help would be appreciated.
It is true. If $x$ is in the domain of $f$ and $g$, then $x=h(y)$ for some $y$. So, $f(h(y))=g(h(y))$. But this means that $f(x)=g(x)$.