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|x| Absolute value property - general question

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Joined: 29 Aug 2012
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|x| Absolute value property - general question [#permalink] New post 30 Oct 2012, 03:58
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Is this true:

Range of values of |x| = x^2
and also |x| = sqrt. x^2
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Re: |x| Absolute value property - general question [#permalink] New post 30 Oct 2012, 04:55
Expert's post
himanshuhpr wrote:
Is this true:

Range of values of |x| = x^2
and also |x| = sqrt. x^2


Point 1 is not clear, what does the range of |x| mean?

As for \sqrt{x^2}=|x|.

Let's consider following examples:
If x=5 --> \sqrt{x^2}=\sqrt{25}=5=x=positive;
If x=-5 --> \sqrt{x^2}=\sqrt{25}=5=-x=positive.

So we got that:
\sqrt{x^2}=x, if x\geq{0};
\sqrt{x^2}=-x, if x<0.

What function does exactly the same thing? The absolute value function: |x|=x, if x\geq{0} and |x|=-x, if x<0. That is why \sqrt{x^2}=|x|.

Hope it's clear.
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Re: |x| Absolute value property - general question   [#permalink] 30 Oct 2012, 04:55
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