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by limestone » Thu Oct 28, 2010 1:53 am
If x<0 then |x| = -x,
then sqrt {(-x)*|x|} = sqrt {(-x)^2}
= sqrt (x^2) = |x|
and |x| = -x

Thus the answer should be A.

Or you can also apply some tips here:

the function contains only x, then the answer cannot be a specific number. Thus the answer cannot be 1 or -1. Eliminate B,C

The square root of a negative number does not exist. Thus eliminate E, sqrt (x) cannot exist as x<0.

Only A and D remain.

The result of a square root is positive, thus D is eliminated as x<0. For example: sqrt(3) = 1.7 not -1.7.

Hence pick A.
Last edited by limestone on Thu Oct 28, 2010 2:05 am, edited 2 times in total.
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by Rahul@gurome » Thu Oct 28, 2010 1:53 am
x < 0 => |x| = -x (Think about it!)

sqrt[(-x)*(|x|)] = sqrt[(-x)*(-x)] = sqrt[x^2] = |x| = -x

The correct answer is A.
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