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KVPY Sample Paper KVPY Stream-SX Model Paper-11

  • question_answer
                Let A =\[\{x\in R:x\] is not a positive integer}. Define a function \[f:A\to R\,\]as \[f(x)=\frac{2x}{x-1}\] then f is:

    A) injective but nor surjective

    B) not injective

    C) surjective but not injective

    D) neither injective nor surjective?

    Correct Answer: A

    Solution :

    \[f(x)=2\left( 1+\frac{1}{x-1} \right)\] \[f'(x)=-\frac{2}{{{(x-1)}^{2}}}\] \[\Rightarrow \]\[f\] is one?one but not onto.


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