Mathematics - Continuity - Differentiability Question with Solution | TestHub

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 _____________