Abstract Algebra: Proof with one-to-one function and function composition

Prove that if f is one-to-one and f∘g=f∘h, then g=h.

[sinamustafa]

Suppose f : A → B and g : B → C are functions. Prove that if g ◦ f is injective
then f is injective. Prove that if g ◦ f is surjective. then g is surjective.