Ali,

If a function f(x) is periodic with period k then for any x, f(x + k) = f(x). So for example if the period is k = 3 and f(2) = 7 then f(5) = f(2 + 3) = f(2) = 7 and also f(8) = f(5 + 3) = f(5) = 7. You can also find f(11) since 11 = 8 + 3 ad so on. So let's try a problem that's similar to the one you sent.

A periodic function f(x) has a period of 7, if f(2 )= -4 and f(3)=12, determine the value of f(17)?

Since the period is 7 and we know the value f(2) = -4 then

f(9) = f(2 + 7) = f(2) = -4
f(16) = f(9 + 7) = f(9) = -4
f(23) = f(16 + 7) = f(16) = -4
and so on...

But we jumped over f(17) which is what we want. So let's start with f(3) = 12.

f(10) = f(3 + 7) = f(3) = 12
f(17) = f(10 + 7) = f(10) = 12

But that is what we want so I know that f(17) = 12.

Now try the problem you sent us,
Penny