Answer
$g(19)=2
,\\\\
g(-13)=\text{does not exist}
,\\\\
g(1)=\text{does not exist}
,\\\\
g(84)=3$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Substitute the given function value in $
g(t)=\sqrt[4]{t-3}
.$
$\bf{\text{Solution Details:}}$
If $
t=19
,$ then
\begin{array}{l}\require{cancel}
g(t)=\sqrt[4]{t-3}
\\\\
g(19)=\sqrt[4]{19-3}
\\\\
g(19)=\sqrt[4]{16}
\\\\
g(19)=2
.\end{array}
If $
t=-13
,$ then
\begin{array}{l}\require{cancel}
g(t)=\sqrt[4]{t-3}
\\\\
g(-13)=\sqrt[4]{-13-3}
\\\\
g(-13)=\sqrt[4]{-16}
\text{ (not a real number)}
.\end{array}
If $
t=1
,$ then
\begin{array}{l}\require{cancel}
g(t)=\sqrt[4]{t-3}
\\\\
g(1)=\sqrt[4]{1-3}
\\\\
g(1)=\sqrt[4]{-2}
\text{ (not a real number)}
.\end{array}
If $
t=84
,$ then
\begin{array}{l}\require{cancel}
g(t)=\sqrt[4]{t-3}
\\\\
g(84)=\sqrt[4]{84-3}
\\\\
g(84)=\sqrt[4]{81}
\\\\
g(84)=3
.\end{array}
Hence,
\begin{array}{l}\require{cancel}
g(19)=2
,\\\\
g(-13)=\text{does not exist}
,\\\\
g(1)=\text{does not exist}
,\\\\
g(84)=3
.\end{array}