Answer
a) 1
b) -1
c) 1
Work Step by Step
(a)
Let us consider the function $f\left( x \right)=\frac{x}{\left| x \right|}$.
By putting the value of $x$ as $6$ in the equation of $f\left( x \right)$ we obtain the value of $f\left( 6 \right)$ as:
$\begin{align}
& f\left( x \right)=\frac{x}{\left| x \right|} \\
& f\left( 6 \right)=\frac{6}{\left| 6 \right|} \\
& =\frac{6}{6} \\
& =1
\end{align}$
Hence, the value of $f\left( 6 \right)$ is $1$.
(b)
Let us consider the function $f\left( x \right)=\frac{x}{\left| x \right|}$.
By putting the value of $x$ as $-6$ in the equation of $f\left( x \right)$ we obtain the value of $f\left( -6 \right)$ as:
$\begin{align}
& f\left( x \right)=\frac{x}{\left| x \right|} \\
& f\left( -6 \right)=\frac{-6}{\left| -6 \right|} \\
& =\frac{-6}{6} \\
& =-1
\end{align}$
Hence, the value of $f\left( -6 \right)$ is $-1$.
(c)
Let us consider the function $f\left( x \right)=\frac{x}{\left| x \right|}$.
By putting the value of $x$ as ${{r}^{2}}$ in the equation of $f\left( x \right)$ we obtain the value of $f\left( {{r}^{2}} \right)$ as:
$\begin{align}
& f\left( x \right)=\frac{x}{\left| x \right|} \\
& f\left( {{r}^{2}} \right)=\frac{{{r}^{2}}}{\left| {{r}^{2}} \right|} \\
& =\frac{{{r}^{2}}}{{{r}^{2}}} \\
& =1
\end{align}$
Hence, the value of $f\left( {{r}^{2}} \right)$ is $1$.
