JEE Math Practice Question

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

1. A.neither one-one nor onto.
2. B.one-one but not onto.
3. C.both one-one and onto.
4. D.onto but not one-one.