Answer
$$y=\sqrt[4]{2}\sqrt[4]{x},\:y=-\sqrt[4]{2}\sqrt[4]{x}$$
Work Step by Step
Switching the elements of the domain and the range (in other words, the dependent and independent variables), we find that the inverse is:
$$x=\frac{1}{2}y^4 \\ y=\sqrt[4]{2}\sqrt[4]{x},\:y=-\sqrt[4]{2}\sqrt[4]{x}$$
