It would seem having $f(x+1)=f(x)$ should just give me a straight line, since say $f(1)=2$,$f(2)=f(1)=2$ etc. So all $x$ are assigned to the one $y$ value, hence (here) I would have the line $y=2$.
What if I have another function with it? E.g I know that
$f(x) = x^2$
$f(x+1) = f(x)$
How do these interact? Do they only interact if I set them up for example:
$f(x) = x^2$, $-5\leq x\leq5$
$f(x+1) = f(x)$, $-\infty \lt x \lt \infty$
How does this look inside $[-5,5]$?
f need not be a constant line at all, how about
Also, two definitions of f which are given contradict each other. f(x+1) = f(x) is clearly periodic with period 1. However, f(x) = x^2 is not periodic anywhere. Did you mean two different functions, f & g?
Also, how do you know that $f(x) = x^2$? This is valid for only a single point of $f(x) = f(x+1)$ namely x= 0 and x+1 = 1