A function f is periodic of period of period 5. If f (3) = 10, f (0) = 13, and f (-5) = 31 then find f (13)

If f (x) is some function with period T, then f (x) = f (x+T) for all x in the domain.

In this case, T = 5 is the period so

f (x) = f (x+5)

f (3) = 10

f (3) = f (3+5) = f (8) = 10

f (8) = f (8+5) = f (13) = 10

Therefore, f (13) = 10

The final answer is 10