Answer
$f(x)=\sqrt[4]{-x}+1$
Work Step by Step
Given the standard function, $
f(x)=\sqrt[4]{x}
$, the equation of the graph that is reflected about the $y-$axis will have a negative multiplier in the $x-$variable. Hence, the equation becomes
\begin{array}{l}\require{cancel}
f(x)=\sqrt[4]{-x}
.\end{array}
Given the function, $
f(x)=\sqrt[4]{-x}
$, the equation of the graph that shifts upward will have a positive constant added to the equation. Hence, a shift of $1$ unit upward will have the equation,
\begin{array}{l}\require{cancel}
f(x)=\sqrt[4]{-x}+1
.\end{array}
