if f(x+5)=f(x) for all values of x, then f(x)=0 for how many different values of x between 0 and 12?

Question

PLEASE explain.

Answer 1

f(x+5)=f(x) for all x means that the function is periodic (and not necessarily constant as other people said). So the function is entirely determined by f(0), f(1), f(2), f(3) and f(4).
But there isn't enough information to answer the question and the answer could be anything between 0 and 13, except 9, 11 and 12.

Answer 2

If f(x+5)=f(x) for all values of x, then f(x)=C where C is a constant. If the constant is set to zero, then there are infinitely many values for which f(x)=0 on that interval, if not, then there are none.

The other alternative is that the function is periodic with period 5, in which case we know even less than if the function is constant.

Answer 3

That's impossible to tell without knowing what the function f is.

Answer 4

(Edit): Oops! It would be a periodic function, not necessarily constant. Sorry bout that. Chaps is right.

Answer 5

the sum of the square of two legs on a right triangle is equal to the square of the coexisting side.

Answer 6

umm.. im going to take a guess and say 5..or 0? idk leave me alone..im not an animal!