Question

What is the equation (simplified) the inverse of y=2x^2?

Answer 1

$2x^2=y\ \ \ |divide\ both\ sides\ by\ 2\\\\x^2=\dfrac{y}{2}\\\\\boxed{x=\sqrt{\frac{y}{2}}}\\\\x=\dfrac{\sqrt{y}}{\sqrt2}=\dfrac{\sqrt{y}\cdot\sqrt2}{\sqrt2\cdot\sqrt2}\to\boxed{x=\dfrac{\sqrt{2y}}{2}}\\\\\\\boxed{f(x)=2x^2\to f^{-1}(x)=\dfrac{\sqrt{2y}}{2}}$