Number of solutions of the function 
Let $'f'$ be an even periodic function with period 4 such that $f(x) = 2^x -1$, $0\le x \le2$. The number of solutions of the equation $f(x) = 1$ in $[-10,20]$ are?

Since the given function is even,
$f(x) = f(-x)$
since the given function is periodic,
$f(x+4) = f(x)$
So,
$f(x+4) = f(-x)$
Well, according to the function defined for $x \in [0,2]$ we get one solution for $f(x) = 1$ at $x=1$
I don't know how do I proceed from here.
Any help would be appreciated. 

First, we observe that as $f$ is even, the solutions $f(x) = 1$ on $[-2,2]$ is 1 and -1. Then, use the periodicity, $f(x+4) = f(x)$ to extend this function to find all the roots in your interval. For instance, we have $f(1) = f(5) = f(9)$ ...
