Suppose r(x) and t(x) are two functions with the same domain, and let h(x)=r(x)+t(x). Suppose also that each of the 3 functions r, t and h, has a maximum value in this domain (i. e. a value that is greater than or equal to all the other values of the function).

Let M = the maximum value of r(x),
N = the maximum value of t(x), and
P = the maximum value of h(x).
How might the following always be true that M+N=P?

Prove the relationship to be true, or state what relationship does exist between the numbers M+N and P.