Let f, g: R → R be defined as: f(x)=|x-1| and g(x)= {e^x, x ≥ 0; x+1, x ≤ 0.} Then the function f(g(x)) is

Let $\displaystyle f, g: \mathbf{R} \rightarrow \mathbf{R}$ be defined as : $\displaystyle f(x)=|x-1|$ and $\displaystyle g(x)= \begin{cases}\mathrm{e}^x, & x \geq 0 \\ x+1, & x \leq 0 .\end{cases}$ Then the function $\displaystyle f(g(x))$ is