<p>If f(x)= (x^2)^1/2, then f(x) can also be expressed as
A. x
B. -x
C. +-x
D. |x|</p>
<p>The answer is d but I don't understand as to why it can't be C. </p>
<p>The x^2 can never be negative. Therefore the square root can only be positive</p>
<p>sqrt(x) or x^(1/2) usually denotes the nonnegative root, i.e. sqrt(81) = 9, sqrt(0) = 0.</p>
<p>Yeah, I thought the answer could be +/- x if you square first and then apply the root, but according to one of the books I read, as far as the SAT is concerned only the positive root is considered, so it would be |x| either way.</p>
<p>Thank you to all of you. </p>
<p>f(x) = sqrt(x^2) is the usual definition of |x|. This definition is equivalent to the piecewise defined definition f(x) = x if x>=0, and f(x) = -x if x<0.</p>
<p>In nonmathematical terms, both of these definitions say “just make the number nonnegative.”</p>
<p>Notice that if x = 1 we have sqrt(x^2) = sqrt(1^2) = sqrt(1) = 1</p>
<p>And if x = -1 we have sqrt(x^2) = sqrt((-1)^2) = sqrt(1) = 1</p>
<p>sqrt(x) ALWAYS means the positive square root of x. That is the standard definition of the square root symbol. If you want the negative square root you need to write -sqrt(x)</p>