Transformation of a variable Let say $x$ is a continuous variable such that $-a\leq x\leq a$, $a>0$. Is there any way to transform this variable so that the resultant variable can take any value in real line?
I am looking for some $1:1$ transformation so that I can also make reverse transformation.

Yes.  Here are several examples:
$$x \rightarrow \tan\left(\frac{\pi x}{2 a}\right).$$
$$x \rightarrow \frac{1}{x/a-1}+\frac{1}{x/a+1}.$$
