JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    The largest possible set of real numbers which can be the domain of \[f(x)=\sqrt{1-\frac{1}{x}}\] is                          [AMU 2000]

    A)                    \[(0,\ 1)\cup (0,\ \infty )\]

    B)             \[(-1,\ 0)\cup (1,\ \infty )\]

    C)            \[(-\infty ,\ -1)\cup (0,\ \infty )\]

    D)            \[(-\infty ,\ 0)\cup (1,\ \infty )\]

    Correct Answer: D

    Solution :

               \[1-\frac{1}{x}>0\Rightarrow x>1\]. Also, \[x\ne 0\].                    \ Required interval \[=(-\infty ,\,0)\cup (1,\,\infty )\].


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