single valued function and multi valued function square root function is a multi valued function. for example 16 have two square root 4 and -4. but it is violation of the definition of function that each element of domain has one and only one image. then how it is a function. please clear my dout.

$f:[0,\infty)\to[0,\infty)$ defined by $f(x)=\sqrt{x}$ assigns to each $x$ a single value, the positive square root. This is a function.
Similarly, $-f$ is a function. 
Functions cannot output more than one value for a given input.
