Answer
a) 3
b) 7
c) $\sqrt{x}+3$
Work Step by Step
(a)
Let us consider the function $f\left( r \right)=\sqrt{r+6}+3$.
By putting the value of $r$ as $-6$ in the equation of $f\left( r \right)$ we obtain the value of $f\left( -6 \right)$ as
$\begin{align}
& f\left( r \right)=\sqrt{r+6}+3 \\
& f\left( -6 \right)=\sqrt{-6+6}+3 \\
& =0+3 \\
& =3
\end{align}$
Hence, the value of $f\left( -6 \right)$ is $3$.
(b)
Let us consider the function $f\left( r \right)=\sqrt{r+6}+3$.
By putting Value of $r$ as $10$ in the equation of $f\left( r \right)$ we obtain the value of $f\left( 10 \right)$ as
$\begin{align}
& f\left( r \right)=\sqrt{r+6}+3 \\
& f\left( 10 \right)=\sqrt{10+6}+3 \\
& =4+3 \\
& =7
\end{align}$
Hence, the value of $f\left( 10 \right)$ is $7$.
(c)
Let us consider the function $f\left( r \right)=\sqrt{r+6}+3$.
By the putting value of $r$ as $x-6$ in the equation of $f\left( r \right)$ we obtain the value of $f\left( x-6 \right)$ as
$\begin{align}
& f\left( r \right)=\sqrt{r+6}+3 \\
& f\left( x-6 \right)=\sqrt{x-6+6}+3 \\
& =\sqrt{x}+3
\end{align}$
Hence, the value of $f\left( x-6 \right)$ is $\sqrt{x}+3$.
