# Math Help - Periodic functions

1. ## Periodic functions

If $f(a-x)=f(a+x);f(b-x)=f(b+x),\forall x\in R, a>b$.Then prove that the function $f(x)$ is periodic and hence find its period.

2. Originally Posted by pankaj
If $f(a-x)=f(a+x);f(b-x)=f(b+x),\forall x\in R, a>b$.Then prove that the function $f(x)$ is periodic and hence find its period.
Let $x = a - t$ so the first gives $f(t) = f(2a - t)$

Let $x = b - t$ so the secondgives $f(t) = f(2b-t)$

Equating gives

Let $f(2a-t) = f(2b-t)$ and setting $T=2a-t$ first gives $f(T) = f(T+2b-2a)$ and so the period is $2b-2a$