i need full solution for this question.

1. In this problem, we will only work with functions with domain R and codomain R. therefore, if we say that two functionsfand g are equal (f = y), it means that Vx E R, f(x) = g(x). We need a new definition. We say that a function f is faithful when \"For every two functionsg and h, f o g = f c h = g = h." (a) Prove that if a function is one to one, then it is faithful. (b) Prove that if a function is NOT one- to- one, then it is NOT faithful