Identity functions are functions that returns the SAME value which was used in its argument. In this case, f(x) = g(x). Therefore f(x) = g(x) = x.
Conditional functions are conditions that evaluates the condition and returns DIFFERENT values all depending on the condition value. That is, in this case, f(x) is not equal to g(x) for every x domain.
So, while identity functions returns the same value, conditional functions returns different functions.
