I can't find a absolute value function that have [-1,1] range

Question

I want a function $f:\mathbb{R}\to[-1,1]$ with absolute value like $f(x)=|a-x|\ldots$ that have $[-1,1]$ range. Can anybody help me?

Answer 1

The question is unclear. Maybe this answer will move you to clarify. Let $f(x)=\sin x$. Then $f$ has domain $\bf R$ and range $[-1,1]$, as you want.

EDIT: Here's one that uses the absolute value function: $$f(x)=-1+{2|x|\over\sqrt{x^2+1}}$$

Answer 2

What i have understood is, For what values of x, the function f(x) belongs to [-1 ,1]. Am I correct???

If it is correct, the answer is, x belongs to [a-1 , a+1].