function question 
$ f(x) = \begin{cases} -1 && \text{for}-2\le x \le0\\ x-1 && \text{for } 0<x\le2
 \end{cases}\\\text{Domain of }f(x) = [-2,2]\\
\text{Let there be be another function g(x),such that}\\
g(x) = f(|x|) + |f(x)| \\
$
$\text{What is function g(x)?}$
I worked the question and got $g(x) = \begin{cases} 
0 & \text{for } 0<x<1 \\ 
 -x & \text{for }-2\le x \le 0 \\
2(x-1) & \text{for } 1\le x \le 2
\end{cases} $
Is there anything wrong with my answer?

There's nothing wrong with your answer.
Case 1. $-2\leq x \leq 0$
\begin{array}{rl}
g(x)&=f(-x) + |f(x)|   \\ 
&=(-x)-1 +|-1|  &     \\ 
&=-x
\end{array} 
Case 2. $0< x < 1$
\begin{array}{rl}
g(x)&=f(x) + |x-1|   \\ 
&=x-1 + [-(x-1)]  &     \\ 
&=x-1-x+1\\
&=0
\end{array} 
Case 3. $1 \leq x \leq 2$
\begin{array}{rl}
g(x)&=f(x) + |x-1|   \\ 
&= x-1 + (x-1)  &     \\ 
&=2(x-1).
\end{array} 
