What is the verification to make y=3x^2 a inverse

Answer 1

y= 3x^2

switch x and y, then solve for the new y

x = 3y^2

y^2 = x/3

y = f^-1(x) = +/-sqr(x/3) = the inverse relation, but not inverse function as it fails the vertical line test

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graph them, the inverse relation is the original function reflected over the line y=x They interest at 2 points, both on the line y=x, one is the vertex at the origin. the 2nd is about (.326, .325) where 3x^2 = sqr(x/3)