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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2009

  • question_answer
    If\[f:R\to R\]and\[g:R\to R\]are denned by \[f(x)=x-3\]and\[g(x)={{x}^{2}}+1,\]then the values of\[x\]for which\[g\{f(x)\}=10\]are

    A)  \[0,-6\]                               

    B)  \[2,-2\]

    C)  \[1,-1\]               

    D)         0, 6

    E)  0, 2

    Correct Answer: D

    Solution :

    Given, \[f(x)=x-3,g(x)={{x}^{2}}+1\] \[\therefore \]  \[g\{f(x)\}=g(x-3)\] \[\Rightarrow \]               \[10={{(x-3)}^{2}}+1\] \[\Rightarrow \]               \[10={{x}^{2}}+10-6x\] \[\Rightarrow \]               \[x(x-6)=0\] \[\Rightarrow \]               \[x=0,6\]


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