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.
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.