Given $f(x) = f(x+2)$ and $f(3)=20$, prove or disprove $f(4)=20$

Given: $$f(x) = f(x+2)$$ $$f(3)=20$$ prove or disprove $f(4)=20$

In my opinion $f(4)$ can have any value according to the question...since the only data is about the odd range values...I thought of a function like $f(x)=(K-20)(-1)^x + K$

• If f(x) = f(x+2) then the function is periodic (compare to sin(x) = sin(x +2pi)). But knowing the value at x=3 doesn't say anything about values other than x = 3+2, 3+4, .... Feb 20, 2014 at 9:51