Let $f(x)=\sqrt[4]{7x+10}.$

$($a$)$ Sort the following operations in the order they are applied to $x$ in $f(x).($Click and drag to sort items.$)q,|$

$($b$)$ Consider the inverse function $f^{-1}(x).$ Sort the following operations in the order they would be applied to $x$ in $f^{-1}(x)$

Raise to $4-$th power

$($c$)$ What is the inverse function $f^{-1}(x)?$

$\{\begin{array}{c}\text{:}{f}^{-1}(x)=\end{array}$