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.
Square root of a function
Re: Square root of a function
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
sqrt (x^2) = |x|