If y^2=x is not a function, how do we find domain and range of that function? But I also saw from a book which found the domain of y = (x)^1/2

Answer 1

y^2 = x is not a function. It's a relation

domain is the values of x = [0, infinity) = any non-negative real number

range is the values of y = any real number (-infinity, +infinity)

y = (x)^1/2 is a function, it's the top half of y^2=x. It's the top half of a rightward opening parabola with vertex at the origin, the point (0,0)

y^2 =x is the same as y= + square root of x = + (x)^1/2 which are not functions, but drop the - square root and it is a function.

the vertical line test means if you can draw a vertical line through the curve, it's not a function. You can draw a vertical line through y^2 = x and cut the curve more than once. But y=sqr(x) is a function, as you cannot cut the curve with a vertical line that cuts the curve in more than one point. the domain of y=sqr(x) is all non-negative real numbers. the range is also all non-negative real numbers