Let $$f(x) = \begin{cases} -a & \text{if } -a \leq x \leq 0 \\ x + a & \text{if } 0 < x \leq a \end{cases}$$ where $$a > 0$$ and $$g(x) = (f(|x|) - |f(x)|)/2$$. Then the function $$g : [-a, a] \rightarrow [-a, a]$$ is :

A

neither one-one nor onto

B

onto

C

both one-one and onto

D

one-one