Functions

Let \(f, g: \mathbf{R} \rightarrow \mathbf{R}\) be defined as :

$$f(x)=|x-1| \text { and } g(x)= \begin{cases}\mathrm{e}^x, & x \geq 0 \\ x+1, & x \leq 0 .\end{cases}$$

Then the function \(f(g(x))\) is