JEE Main & Advanced Sample Paper JEE Main Sample Paper-47

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

    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 \[x=\frac{3\pi }{4},\,\,\frac{7\pi }{4}\]

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