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J & K CET Engineering J and K - CET Engineering Solved Paper-2011

  • question_answer
    If \[f(x)=3-x,-4\le x\le 4,\]then the domain of \[{{\log }_{e}}\,(f\,(x))\] is

    A)  \[[-4,\,\,4]\]      

    B)  \[(-\,\infty ,\,\,3]\]

    C)  \[(-\,\infty ,\,\,3)\]

    D)  \[[-4,\,\,\,3)\]

    Correct Answer: C

    Solution :

    Given,   \[f(x)=3-x,\,\,-4\le x\le 4\] Now, \[{{\log }_{e}}\,f\{(x)\}=lo{{g}_{e}}\,(3-x)\] Here, existance for the above function \[3-x>0\] \[\Rightarrow \] \[x-3<0\] \[\Rightarrow \] \[x<3\] So, the domain of \[{{\log }_{e}}\,\{f\,(x)\,\}\] is \[(-\infty ,\,3).\]


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