inverse of y=(1/4)cos^(-1)2x

$$\\y=\dfrac{1}{4}*\cos^{-1}(2x)\\ \mbox{Now change y and x }\quad \textcolor[rgb]{1,0,0}{x}=\dfrac{1}{4}*\cos^{-1}(2\textcolor[rgb]{1,0,0}{y})\\ 4x=\cos^{-1}(2y)\quad | \quad \cos\\$$

$$\\\cos{(4x)}= 2y\\ 2y = \cos{(4x)} \quad | \quad :2\\ \boxed{y=\dfrac{1}{2}*\cos{(4x)}} \quad inverse$$