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) \[\left\{ \frac{5\pi }{4},\,\frac{7\pi }{3} \right\}\]
Correct Answer: B
Solution :
\[f\left\{ g(x) \right\}=\,\left\{ \begin{matrix} 1,\,0<x<\frac{3\pi }{4}\,or\,\frac{7\pi }{4}<x<2\pi \\ 0,x=\frac{3\pi }{4},\,\,\frac{7\pi }{4} \\ -1,\,\,\frac{3\pi }{4}<x<\frac{7\pi }{4} \\ \end{matrix} \right.\]Clearly, \[f[g(x)]\] is not continuous at \[x=\frac{3\pi }{4},\,\,\frac{7\pi }{4}\]You need to login to perform this action.
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