What is the Proof for f=h when fog=x and goh=x in Composition?

[STEMucator]

Homework Statement

Can't believe I forgot how to do this...

Prove if fog = x and goh = x then f=h for all x.

Homework Equations

Obviously the associativity of composition here.

The Attempt at a Solution

So we know :

fog = goh
fogoh = gohoh
fo(goh) = (goh)oh

I've forgotten how to do the rest here.

 

[STEMucator]

Any pointers at all?

 

[jbunniii]

$h = (f \circ g) \circ h = \ldots$