Suppose r(x) and t(x) are two functions with the same domain, and let h(x)=r(x)+t(x)

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.