• # question_answer Let $f(x)=\,\left\{ \begin{matrix} -1,\,x<0 \\ 0,\,x=0 \\ 1,\,x>0 \\ \end{matrix} \right.$ and $g(x)=\sin \,x+\cos \,x,$ then points of discontinuity of $f\{g(x)\}$ in $(0,\,2\pi )$ is A)  $\left\{ \frac{\pi }{2},\,\frac{3\pi }{4} \right\}$                    B)  $\left\{ \frac{3\pi }{4},\,\frac{7\pi }{4} \right\}$ C)  $\left\{ \frac{2\pi }{3},\,\frac{5\pi }{3} \right\}$                  D)  $\left\{ \frac{5\pi }{4},\,\frac{7\pi }{3} \right\}$

$f\left\{ g(x) \right\}=\,\left\{ \begin{matrix} 1,\,0<x<\frac{3\pi }{4}\,or\,\frac{7\pi }{4}<x<2\pi \\ 0,x=\frac{3\pi }{4},\,\,\frac{7\pi }{4} \\ -1,\,\,\frac{3\pi }{4}<x<\frac{7\pi }{4} \\ \end{matrix} \right.$Clearly, $f[g(x)]$ is not continuous at $x=\frac{3\pi }{4},\,\,\frac{7\pi }{4}$