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

[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?

 

[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 $\pm\sqrt x$.