Question

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)

Answer 1

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