How to invert this function? (Inverse exponential function with arctan)

Question

How to invert this function? $$ y = e^{\arctan(x^5)} $$

Answer 1

$\newcommand{\leftlong}{\longleftarrow\!\shortmid}$ What gets done last gets undone first: $$ \begin{array}{rcccccl} x & \longmapsto & x^5 & \longmapsto & \arctan(x^5) & \longmapsto & \exp(\arctan(x^5)) = y \\[12pt] \sqrt[5]{\tan(\log_e y)} & \leftlong & \tan(\log_e y) & \leftlong & \log_e y & \leftlong & y \end{array} $$

Answer 2

I guess by "solve", you mean "find the inverse $x=f(y)$".

$$y=e^{\arctan(x^{5})}\Leftrightarrow \log{y}=\arctan(x^{5})\Leftrightarrow \tan{(\log{y})}=x^{5}\Leftrightarrow(\tan(\log{y}))^{1/5}=x.$$

Answer 3

$${}x=\sqrt[5]{\tan(\log y)}$$