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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-2

  • question_answer
    The domain of the function \[\mathbf{f}\left( \mathbf{x} \right)=\mathbf{lo}{{\mathbf{g}}_{10}}\left( \sqrt{\mathbf{x}-\mathbf{4}}\text{ }+\sqrt{\mathbf{6}-\mathbf{x}} \right)\]is

    A)   \[\left[ 4,6 \right]\]                    

    B)  \[\left( 2,6 \right)\]         

    C)  \[\left[ 4,6 \right)\]                     

    D)  \[\left( 4,6 \right]\]

    Correct Answer: A

    Solution :

    [a] \[\because f(x)=lo{{g}_{10}}\left( \sqrt{x-4}+\sqrt{6-x} \right)\] For defining the function. Again, \[x-4\ge 0\Rightarrow x\ge 4\] and\[\sqrt{6-x}\ge 0\] \[\Rightarrow 6-x\ge 0\Rightarrow x\le 6\] Hence, domain of\[f=\left[ 4,\infty  \right]\cap \left[ -\infty ,6 \right]\]                         \[=\left[ 4,\text{ }6 \right]\] Hence, option [a] is correct.


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