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