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Math Help - Inverse Function Help

  1. #1
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    Inverse Function Help

    Hi, I have this question that I can't seem to work out.

    f(x) = 6x + 7x^{19}
    I need to find a = f^{-1}(c) where c = -13

    I can't seem to work out an inverse function.
    I tried to say

    f(f^{-1}(-13)) = -13 = 6f^{-1}(-13) + 7(f^{-1}(-13))^{19}
    -13 = 6a + 7a^{19}

    But how can I solve for a?
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  2. #2
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    Quote Originally Posted by alan4cult View Post
    Hi, I have this question that I can't seem to work out.

    f(x) = 6x + 7x^{19}
    I need to find a = f^{-1}(c) where c = -13

    I can't seem to work out an inverse function.
    I tried to say

    f(f^{-1}(-13)) = -13 = 6f^{-1}(-13) + 7(f^{-1}(-13))^{19}
    -13 = 6a + 7a^{19}

    But how can I solve for a?

    You have the polynomial equation

    7a^{19}+6a+13=0

    From the rational roots theorem we now the only root are the factors of
    13 \{\pm 1,\pm 13 \} divided by the factors of 7 \{\pm 1, \pm 7 \}

    So if we check this finite list we see that

    7(-1)^{19}+6(-1)+13=0 this tells us that -1 is a solution to the equation.

    We know this is the only solution because the derivative of f is alwasy posative so the function is 1-1.

    Good luck. TES
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