Let f: R → R and g: R → R be defined as f(x)= {log_e x, x>0; e^-x, x ≤ 0} and g(x)= {x, x ≥ 0; e^x, x<0}. Then, gof: R → R is:

Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ and $\displaystyle g: \mathbf{R} \rightarrow \mathbf{R}$ be defined as $\displaystyle f(x)=\left\{\begin{array}{ll}\log _{\mathrm{e}} x, & x>0 \\ \mathrm{e}^{-x}, & x \leq 0\end{array}\right.$ and $\displaystyle g(x)=\left\{\begin{array}{l}x, x \geqslant 0 \\ \mathrm{e}^x, x<0\end{array}\right.$. Then, gof: $\displaystyle \mathrm{R} \rightarrow \mathrm{R}$ is :