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Show that the function f: R(**)to R (**)...

Show that the function `f: R_(**)to R _(**)` defined by `f (x) = 1/x` is one-one and onto, where `R _(**)` is the set of all non-zero numbes. Is the result true, if the domain `R _(**)` is replaced by N with co-domain being same as `R_(**)` ?

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The correct Answer is:
NO
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Knowledge Check

  • Let the function f : R to R be defined by f(x)= 2x + cos x , then f(x)-

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    one-one and onto
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    D
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  • If the function f: R to R is defined by f(x)=x^(2)-6x-14 , then f^(-1)(2) is equal to -

    A
    {2, 8}
    B
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    D
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