Problem on topology and mapping functions

Question

Assignment:

Let X be a non-empty set. The identity mapping i_x on X is the mapping of X onto itself  defined by i_x(x) = x for every x. Thus i_x sends each element of X to itself; that is, it leaves fixed each element of X. Show that fi_x = i_xf = f for any mapping f of X into itself.

Provide complete and step by step solution for the question and show calculations and use formulas.