Cancellation law with surjective functions

[annoymage]

Homework Statement

suppose function f : A \to B, g: A \to B, h : B \to C satisfy g \circ f=h \circ f. If is surjective then prove that g=h

Homework Equations

n/a

The Attempt at a Solution

so for any x \in A, gf(x)=hf(x), and for any b \in B there exist a \in A, such that f(b)=a

so g(a)=h(a) so g=h is this correct and sufficient?

i'm suppose to to show for any v \in B, g(v)=h(v). i don't know but something's missing.

 

[vela]

You need to clean it up a bit. For one thing, you have g mapping A to B. You meant B to C, right? Also, the element a in in A, but h is defined on B, so when you say h(a), it's not clear that h(a) is defined.