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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 9

  • question_answer
    If \[f(x)=\sqrt[3]{\frac{9}{{{\log }_{2}}(3-2x)}-1},\] then the value of 'a ' which satisfies \[{{f}^{-1}}(2a-4)=\frac{1}{2},\] is

    A) \[1\]                 

    B) \[2\]

    C) \[3\]     

    D) \[4\]

    Correct Answer: C

    Solution :

    [c] Given  \[{{f}^{-1}}(2a-4)=\frac{1}{2}\] \[\therefore \,\,\,\,f\left( \frac{1}{2} \right)=2a-4\] Put  \[x=\frac{1}{2}\] in \[f(x)=\sqrt[3]{\frac{9}{{{\log }_{2}}(3-2x)}-1}\] \[\Rightarrow \,\,\,\,\,f\left( \frac{1}{2} \right)=\sqrt[3]{9-1}=2\] \[\therefore \,\,\,2a-4=2\] \[\Rightarrow \,\,\,\,a=3\]


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