Answer
a) -3
b) 1
c) $\sqrt{2x}-6$
Work Step by Step
(a)
Let us consider the function $f\left( r \right)=\sqrt{25-r}-6$.
By putting the value of $r$ as $16$ in the equation of $f\left( r \right)$ we obtain the value of $f\left( 16 \right)$ as
$\begin{align}
& f\left( r \right)=\sqrt{25-r}-6 \\
& f\left( 16 \right)=\sqrt{25-16}-6 \\
& =3-6 \\
& =-3
\end{align}$
Hence, the value of $f\left( 16 \right)$ is $-3$.
(b)
Let us consider the function $f\left( r \right)=\sqrt{25-r}-6$.
By putting the value of $r$ as $-24$ in the equation of $f\left( r \right)$ we obtain the value of $f\left( -24 \right)$ as
$\begin{align}
& f\left( r \right)=\sqrt{25-r}-6 \\
& f\left( -24 \right)=\sqrt{25-\left( -24 \right)}-6 \\
& =\sqrt{49}-6 \\
& =1
\end{align}$
Hence, the value of $f\left( -24 \right)$ is $1$.
(c)
Let us consider the function $f\left( r \right)=\sqrt{25-r}-6$.
Putting the value of $r$ as $25-2x$ in the equation of $f\left( r \right)$ we obtain the value of $f\left( 25-2x \right)$ as
$\begin{align}
& f\left( r \right)=\sqrt{25-r}-6 \\
& f\left( 25-2x \right)=\sqrt{25-\left( 25-2x \right)}-6 \\
& =\sqrt{25-25+2x}-6 \\
& =\sqrt{2x}-6
\end{align}$
Therefore, the value of $f\left( 25-2x \right)$ is $\sqrt{2x}-6$.
