Answer
The graphs of both functions are not the same.
Work Step by Step
Given
\begin{equation}
\begin{aligned}
& (\sqrt{x}+1)^2=x+1 \\
& {[0,8,1] \text { by }[0,15,1]}
\end{aligned}
\end{equation}
Let
\begin{equation}
\begin{aligned}
f(x)&= (\sqrt{x}+1)^2 \\
g(x)&=x+1\\
\end{aligned}
\end{equation}
The graphs of both functions are shown in the figure and are clearly not the same. They will be identical if we choose:
\begin{equation}
\begin{aligned}
g(x) & =(\sqrt{x}+1)^2 \\
& =x+2\sqrt{x}+1
\end{aligned}
\end{equation}
