If $f(x)$ is the signum function,then in terms of $f(x)$,the constant function $g(x)=1, \forall x \in R$ is
- A$g(x)= \begin{cases}2-f(x), & x < 0 \\ f(x), & x \geq 0\end{cases}$
- B$g(x)= \begin{cases}f(x)+f(-x), & x < 0 \\ f(x) f(-x), & x \geq 0\end{cases}$
- C$g(x)= \begin{cases}1+f(x), & x>0 \\ 1-f(x), & x \leq 0\end{cases}$
- D$g(x)= \begin{cases}f(x)+2, & x < 0 \\ 1+f(x), & x=0 \\ f(x), & x>0\end{cases}$
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