the given function is y² = x;

since y can not be a function;

for the existence of a function, at a single value of domain there is only one value corresponding in range.

if we consider y as a function; given y² = x;

here domain is x and at every value of x there are two values of y. it is a parabola which is on the +x axis to +y axis and -y axis.( on the right side of quadrants and above and below).

we can take example at x = 4; y = +2, -2

it means that function can be define only when at one value of x there will be a unique value in y. there will be not more than one value.

so y² = x can not be a function.