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JCECE Engineering JCECE Engineering Solved Paper-2008

  • question_answer
    Let the functions \[f,\,\,\,g,\,\,\,h\] are defined from the set of real numbers \[R\] to \[R\] such that  \[f(x)={{x}^{2}}-1,\,\,g(x)=\sqrt{({{x}^{2}}+1)}\]and \[h(x)=\left\{ \begin{matrix}   0,if & x\le 0  \\    x,if & x\ge 0  \\ \end{matrix} \right.\], then \[ho(fog)(x)\]is defined by

    A) \[x\]                                     

    B) \[{{x}^{2}}\]

    C) \[0\]                                     

    D)  None of these

    Correct Answer: B

    Solution :

    Given that,\[f(x)={{x}^{2}}-1,\,\,g(x)=\sqrt{({{x}^{2}}+1)}\] and        \[h(x)=\left\{ \begin{matrix}    0,if & x<0  \\    x,if & x\ge 0  \\ \end{matrix} \right.\] \[\therefore \]  \[ho(fog)(x)=hof\{g(x)\}\]                 \[=hof\{\sqrt{({{x}^{2}}+1)}\}\]                 \[=h\{{{(\sqrt{{{x}^{2}}+1})}^{2}}-1\}\]                 \[=h\{{{x}^{2}}+1-1\}\]                 \[=h\{{{x}^{2}}\}\]                 \[={{x}^{2}}\]


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