Let f, g: R → R be functions defined by f(x)={ [x], x<0; |1-x|, x ≥ 0 and g(x)= {e^x-x, x<0; (x-1)^2-1, x ≥ 0}. where [x] denote the greatest integer…

Let $\displaystyle f, g: \mathbf{R} \rightarrow \mathbf{R}$ be functions defined by $$f(x)=\left\{\begin{array}{ll} {[x],} & x<0 \\ |1-x|, & x \geqslant 0 \end{array} \text { and } g(x)= \begin{cases}\mathrm{e}^x-x, & x<0 \\ (x-1)^2-1, & x \geqslant 0\end{cases}\right. $$ where $\displaystyle [x]$ denote the greatest integer less than or equal to $\displaystyle x$. Then, the function $\displaystyle f \circ g$ is discontinuous at exactly :