Answer
$p(4)=\text{does not exist}
,\\\\
p(10)=0
,\\\\
p(12)=2
,\\\\
p(0)=\text{does not exist}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Substitute the given function value in $
p(z)=\sqrt{2z-20}
.$
$\bf{\text{Solution Details:}}$
If $
z=4
,$ then
\begin{array}{l}\require{cancel}
p(z)=\sqrt{2z-20}
\\\\
p(4)=\sqrt{2(4)-20}
\\\\
p(4)=\sqrt{-12}
\text{ (not a real number)}
.\end{array}
If $
z=10
,$ then
\begin{array}{l}\require{cancel}
p(z)=\sqrt{2z-20}
\\\\
p(10)=\sqrt{2(10)-20}
\\\\
p(10)=\sqrt{0}
\\\\
p(10)=0
.\end{array}
If $
z=12
,$ then
\begin{array}{l}\require{cancel}
p(z)=\sqrt{2z-20}
\\\\
p(12)=\sqrt{2(12)-20}
\\\\
p(12)=\sqrt{4}
\\\\
p(12)=2
.\end{array}
If $
z=0
,$ then
\begin{array}{l}\require{cancel}
p(z)=\sqrt{2z-20}
\\\\
p(0)=\sqrt{2(0)-20}
\\\\
p(0)=\sqrt{-20}
\text{ (not a real number)}
.\end{array}
Hence,
\begin{array}{l}\require{cancel}
p(4)=\text{does not exist}
,\\\\
p(10)=0
,\\\\
p(12)=2
,\\\\
p(0)=\text{does not exist}
.\end{array}
