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JEE Main & Advanced Mathematics Functions Question Bank Critical Thinking

  • question_answer
    The domain of the function \[f(x)=\frac{1}{{{\log }_{10}}(1-x)}+\sqrt{x+2}\] is [DCE 2000]

    A) \[]-3,\ -2.5[\cup ]-2.5,\ -2[\]

    B) \[[-2,\ 0[\cup ]0,\ 1[\]

    C) ]0,1[

    D) None of these

    Correct Answer: B

    Solution :

    • \[x+2\ge 0\] i.e., \[x\ge -2\text{ or }-2\le x\]           
    • \[\because {{\log }_{10}}(1-x)\ne 0\] Þ \[1-x\ne 1\]Þ \[x\ne 0\]           
    • Again \[1-x>0\] Þ \[1>x\] Þ \[x<1\]                   
    • All these can be combined as \[-2\le x<0\]
    • and \[0<x<1\].


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