Answer
a) 1;
b) -1;
c) $\begin{cases}
-1,\text{ if }x\lt 1\\
1,\text{ if }x\gt 1
\end{cases}$
Work Step by Step
We are given the function:
$f(x)=\dfrac{|x|}{x}$
a) Compute $f(2)$:
$f(2)=\dfrac{|2|}{2}=\dfrac{2}{2}=1$
b) Compute $f(-2)$:
$f(-2)=\dfrac{|-2|}{-2}=\dfrac{2}{-2}=-1$
c) Compute $f(x-1)$:
$f(x-1)=\dfrac{|x-1|}{x-1}=\begin{cases}
\dfrac{-(x-1)}{x-1},\text{ if }x\lt 1\\
\dfrac{x-1}{x-1},\text{ if }x\gt 1
\end{cases}$
$=\begin{cases}
-1,\text{ if }x\lt 1\\
1,\text{ if }x\gt 1
\end{cases}$
