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If f : R - (-1,1) to R is defined by f(x...

If f : R - (-1,1) `to` R is defined by f(x) = `(x)/(x^(2)-1)`, verify whether f is one to one.

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If f:RR-{-1,1}toRR is defined by f(x)=x/(x^(2)-1) , verify whether f is one to one or nto.

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Knowledge Check

  • F : R to R defined by f (x) = (1)/(2x^2 +5) the range of F is

    A
    A. `(5,oo)`
    B
    B. `[0,1/5]`
    C
    C. `[1/5 ,5]`
    D
    D. none of these

  • If f : R to R is given by f(x) = 3x-5, then f^(-1) (x) is

    A
    `(1)/(3x-5)`
    B
    `(x+5)/(3)`
    C
    does not exist since f is not one-one
    D
    does not exists since f is not onto

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    If f:R to R is defined by f(x) = 3x - 5 , prove that f is a bijection and find its inverse .

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