elementary set theory - How do you prove that this function is bijective?

How do you prove that this function is bijective?
$f\colon (0,1)\longrightarrow \mathbb{R}$
$f(x)=\tan (\pi(x-1/2))$
In fact I want to show that $(0,1)$ is equivalent to $\mathbb{R}$ by proving that $f$ is bijective. Using Derivative concept and the Intermediate value theorem, it's easy to prove that is bijective, but I'm not allowed to use them.