Let f(x)= {e^x-1, x<0; x^2-5 x+6, x ≥ 0} and g(x)=f(|x|)+|f(x)|. If the number of points where g is not continuous and is not differentiable are α…

Let $\displaystyle f(x)=\left\{\begin{array}{cc}e^{x-1} & , x<0 \\ x^2-5 x+6 & , x \geq 0\end{array}\right.$ and $\displaystyle g(x)=f(|x|)+|f(x)|$. If the number of points where $\displaystyle g$ is not continuous and is not differentiable are $\displaystyle \alpha$ and $\displaystyle \beta$ respectively, then $\displaystyle \alpha+\beta$ is equal to $\displaystyle \_\_\_\_$