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If $f(x)=\left\{\begin{array}{cc}2 x+1 & \text { if } x \leq 0 \\ x+2 & \text { if } x>0\end{array}\right.$ then $$f^{-1}(x)=$$
Select one: a. $\left\{\begin{array}{ccc}\frac{1}{2}(x-1) & \text { if } & x<1 \\ x-2 & \text { if } & x \geq 2\end{array}\right.$ b. $\left\{\begin{array}{rll}\frac{1}{2}(x-1) & \text { if } & x \leq 0 \\ x-2 & \text { if } & x>0\end{array}\right.$ c. $\left\{\begin{array}{cl}\frac{1}{2}(x-1) & \text { if } x<0 \\ x-2 & \text { if } x \geq 0\end{array}\right.$ d. $\left\{\begin{array}{ccc}\frac{1}{2}(x-1) & \text { if } & x \leq 1 \\ x-2 & \text { if } & x>2\end{array}\right.$
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