Continuity and Differenti question bank (Maths)

Let the functions $f:\left(-1,1\right)\to \mathrm{ℝ}$ and  $g:\left(-1,1\right)\to \left(-1,1\right)$ be defined by $f\left(x\right)= \left|2x-1\right|+\left|2x+1\right| \& g\left(x\right)=x-\left[x\right]$, where $\left[x\right]$ denotes the greatest integer less than or equal to$x$. Let $f\circ g:\left(-1,1\right)\to \mathrm{ℝ}$ be the composite function defined by $\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)$. Suppose $c$ is the number of points in the interval $\left(-1,1\right)$ at which $f\circ g$ is not continuous, and suppose $d$ is the number of points in the interval $\left(-1, 1\right)$ at which  $f\circ g$ is not differentiable. Then the value of $c+d$ is _____________

Let $f_1: \mathbb{R}\to \mathbb{R}, f_2\left(-\frac{\pi }{2},\frac{\pi }{2} \right)\to \mathbb{R}, f_3:\left(-1, e^{\frac{\pi }{2}}-2\right)\to \mathbb{R}$ and $f_4: \mathrm{ℝ}\to \mathrm{ℝ}$ be functions defined by
(i) $f_1\left(x\right)=\sin \left(\sqrt{1-e^{-x^2}}\right)$
(ii) $f_2\left(x\right)=\left\{\begin{array}{ll}\frac{\left|\sin x\right|}{{\tan }^{-1}\left(x\right)}& , x\ne 0\\ 1& , x=0\end{array}\right.$ , where the inverse trigonometric function ${\tan }^{-1}x$ assumes values in $\left(-\frac{\pi }{2},\frac{\pi }{2}\right)$
(iii) $f_3\left(x\right)=\left[\sin \left({\log }_{\text{e}}\left(x+2\right)\right)\right]$ , where, for $t\in R, \left[t\right]$ denotes the greatest integer less than or equal to $t$ ,
(iv) $f_4\left(x\right)=\left\{\begin{array}{cc}{x}^2\sin \left(\frac{1}{x}\right) & , x\ne 0\\ 0 & , x=0\end{array}\right.$