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JEE Main & Advanced AIEEE Solved Paper-2002

  • question_answer
    The domain of definition of the function\[f(x)=\sqrt{{{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right)}\] is   AIEEE  Solved  Paper-2002

    A) [1, 4]         

    B)                           [1, 0]                        

    C)           [0, 5]                        

    D)           [5, 0]

    Correct Answer: A

    Solution :

    Since, \[f(x)=\sqrt{{{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right)}\] \[\therefore \,f(x)\] exists only for                    \[{{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right)\ge 0\] \[\Rightarrow \]   \[\frac{5x-{{x}^{2}}}{4}\ge 1\] \[\Rightarrow \]   \[{{x}^{2}}-5x+4\le 0\] \[\Rightarrow \]   \[(x-1)(x-4)\le 0\] \[\Rightarrow \]   \[x\in [1,4]\]


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