How is f(x)=sqrt(x) a valid function?

1. Sep 5, 2014

CuriousBanker

Hello

My teacher has told me the square root function is a valid function. He has also told me that a function cannot possibly have two different output for one given input. 36^1/2 for instance has both -6 and +6 as answers. He told me to just refer to the positive square root...eh, that seems kind of sloppy to just ignore half of the answers out of convenience, no?

2. Sep 5, 2014

DrewD

$\sqrt x$ is defined to be the positive number $a$ such that $a^2=x$. It isn't ignoring half the answers unless you are asked for the numbers $a$ that solve the equation $a^2=x$ and give the answer $\sqrt x$ instead of $\pm\sqrt x$.