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### Square root of a function

Posted: Thu Aug 29, 2013 7:14 am
Hi, it suddenly struck me as to what is meant by the square root of a given function $f$. This should be a precalculus question, but I realize I never paid attention to what it really meant. It occurs in the GRE Math Subject sample test.

So, given a function $f$ on the real line, what does $\sqrt{f}$ mean?

For instance, if $f(x)=(-x)^2=x^2$, does $\sqrt{f}=-x$ or $x$?

*I couldn't find a satisfactory answer on the internet and looking up textbooks didn't seem to yield helpful result either.

### Re: Square root of a function

Posted: Thu Aug 29, 2013 9:36 am
As a general rule, the square root symbol denotes the positive value, whereas the 1/2 power denotes the set of both.

### Re: Square root of a function

Posted: Thu Aug 14, 2014 6:36 pm
sqrt (x^2) = |x|