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J & K CET Engineering J and K - CET Engineering Solved Paper-2010

  • question_answer
    The domain of the function \[f(x)=\frac{1}{{{\log }_{10}}\,(1-x)}\]is

    A)  \[(-\infty ,\,1]\,-\{0\}\]

    B)  \[(-\infty ,\,1)\,-\{0\}\]

    C)  \[(-\infty ,\,\,2)\,\]

    D)  \[(0,\,-\infty )\,\]

    Correct Answer: B

    Solution :

    Given, function \[f(x)=\frac{1}{{{\log }_{10}}\,(1-x)}\] Here, it should be that \[1-x>0\] \[1>x\] \[\Rightarrow \] \[x<1\] Also,  \[x<1\] since, \[f(x)\to \infty \] as \[x\to 0\] \[\therefore \]  Domain of f \[f(x)=(-\infty ,\,1)-\{0\}\]


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