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If R, is the set of all non - negative r...

If R, is the set of all non - negative real numbers prove that the function `f:R_(+) to [-5, infty]" defined by "f(x)=9x^(2)+6x-5` is invertible. Write also `f^(-1)(x)`.

Text Solution

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The correct Answer is:
`f^(-1)x=(sqrt(x+6)-1)/3forall x e in R_(f) = [-5, infty)`
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If R_(+) is the set of all non-negative real numbers prove that the f:R_(+) to (-5, infty) defined by f(x)=9x^(2)+6x-5 is invertible. 39. Write also, f^(-1)(x) .

If R, is the set of all non-negative real numbers prove that the f : R, to [-5, oo) defined by f(x) = 9x^(2) + 6x - 5 is invertible. Write also f^(-1)(x) .

Knowledge Check

  • If R denotes the set of all real numbers then the function f: RtoR defined f(x) = |x|

    A
    one-one only
    B
    onto only
    C
    both one-one & onto
    D
    neither one-one nor onto

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