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)  \[\left\{ \frac{5\pi }{4},\,\frac{7\pi }{3} \right\}\]