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|x| Absolute value property - general question

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Intern
Joined: 29 Aug 2012
Posts: 26

Kudos [?]: 36 [0], given: 56

Schools: Babson '14
GMAT Date: 02-28-2013
|x| Absolute value property - general question [#permalink]

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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

Kudos [?]: 36 [0], given: 56

Math Expert
Joined: 02 Sep 2009
Posts: 42599

Kudos [?]: 135577 [0], given: 12701

Re: |x| Absolute value property - general question [#permalink]

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30 Oct 2012, 04:55
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.
_________________

Kudos [?]: 135577 [0], given: 12701

Re: |x| Absolute value property - general question   [#permalink] 30 Oct 2012, 04:55
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