Is x equals the square root of y-4 a function?

Answer 1

The square root operation is not a function because for each value of y there can be 2 values of x - the principal square root and its negative. This can only be rectified by limiting the range of the opearation to the principal or positive square root.

Furthermore, it also depends on the domain of the function. If y<4 then the square root is not defined within Real numbers.

So, for y ≥ 4, x = +sqrt(y-4) is a function.