simple Pure Mathematics proofs: left and right inverse of composite functions help?

Let f : A -> B and g : B -> C be two functions.
a) Prove that if g ○ f has a left inverse, then f has a left inverse.
b) Prove that if g ○ f has a right inverse, then g has a right inverse.

I have spent about 4 total hours just manipulating the properties of these functions, and I can not come to a conclusion. I realize that these are probably very simple, but I am effectively stumped. Can anyone help?

consider that if w is the left inverse of [ g o f] then w o [ g o f ] = [w o g ] o f = identity