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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?

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    It would help if you elaborated on why you want such a function and what you intend to do with it.2012-04-05

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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: $f(x)=-1+{2|x|\over\sqrt{x^2+1}}$

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    You don't seem to be getting the idea. Nobody knows what you mean! No one is going to be able to help you until you explain what you want, and that explanation has to be more than just an inane repetition of the phrase, "absolute value!".2012-04-10
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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].

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    absolute value function!2012-04-06