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12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-1

  • question_answer
    Domain of the function \[f(x)=lo{{g}_{2}}\left( -{{\log }_{1/2}}\left( 1+\frac{1}{4\sqrt{x}} \right)-1 \right)\]is

    A)  \[\left( 0,1 \right)\]                     

    B) \[(0,1]\]          

    C) \[\left[ 1,\infty  \right)\]                            

    D) \[(1,\infty )\]

    Correct Answer: A

    Solution :

    [a] f is defined if- \[{{\log }_{1/2}}\left( 1+\frac{1}{4\sqrt{x}} \right)-1>0\] i.e., if \[{{\log }_{1/2}}\left( 1+\frac{1}{4\sqrt{x}} \right)<-1\] i.e., if    \[\left( 1+\frac{1}{4\sqrt{x}} \right)>{{\left( \frac{1}{2} \right)}^{-1}}\] i.e., if \[\frac{1}{4\sqrt{x}}>1,\] i.e, \[4\sqrt{x}<1\] i.e. if \[0<x<1\]


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