Answer
$\textbf{a.}\sqrt {x+1}$
$\textbf{b.}\sqrt x+1$
Work Step by Step
$f(x)=\sqrt x$ and $g(x)=x+1$
$\begin{align}
\textbf{a.}(f\bullet g)(x)&=f(g(x))\\&=f(x+1)\\&=\sqrt {x+1}
\end{align}$
$\begin{align}
\textbf{b.}(g\bullet f)(x)&=g(f(x))\\&=g(\sqrt x)\\&=\sqrt x+1
\end{align}$
