KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    Let \[f\,(x)=lo{{g}_{0.5}}\,({{x}^{2}}-5x+6),\] then \[f\,(x)\] is:

    A) one - one but not onto

    B) one - one and onto

    C) onto but not one - one

    D) neither one - one nor onto

    Correct Answer: C

    Solution :

    \[\because \]\[f\,(x)={{\log }_{0.5}}\,({{x}^{2}}-5x+6)\]\[\Rightarrow \]f(x) will be defined if \[{{x}^{2}}-5x+6>0\]\[\Rightarrow \]\[(x-2)\,\,(x-3)>0\]
    from graph of f(x) we can say that it will be a many-one and onto function.

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