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JEE Main & Advanced Mathematics Functions Question Bank Self Evaluation Test - Relation and Functions-II

  • question_answer
    If \[f:R\to R,f(x)=\left\{ \begin{matrix}    x\left| x \right|-4,x\in Q  \\    x\left| x \right|-\sqrt{3}\,x\notin Q  \\ \end{matrix}, \right.\] then \[f(x)\] is

    A) one to one and onto

    B) Many to one and onto

    C) one to one and into

    D) Many to one and into

    Correct Answer: D

    Solution :

    [d] \[f(2)=f\left( {{3}^{1/4}} \right)\Rightarrow \]many to one function And \[f(x)\ne -\sqrt{3}\forall x\in R\Rightarrow \]into function


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