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JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    Let the function \[f:R\to R\] be defined by \[f(x)=2x+\sin x,\ x\in R\]. Then f is [IIT Screening 2002]

    A)            One-to-one and onto      

    B)                    One-to-one but not onto

    C)            Onto but not one-to-one

    D)            Neither one-to-one nor onto

    Correct Answer: A

    Solution :

               \[{f}'(x)=2+\cos x>0\]. So, \[f(x)\] is strictly monotonic increasing so, \[f(x)\] is one-to-one and onto.


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