Question: Given that

\[f\left( x \right)=\left\{ \begin{aligned} & x\text{ }\,\,\,\text{if }x\le 0 \\ & -1\,\,\,\,\,\text{if }x>0 \\ \end{aligned} \right.\] \[g\left( x \right)=\left\{ \begin{aligned} & -x\text{ }\,\,\,\text{if }x<1 \\ & {{x}^{2}}\,\,\,\,\,\text{if }x\ge 1 \\ \end{aligned} \right.\]

Find (a) \(f+g\), (b) \(f-g\), (c) \(fg\).