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Thread: Inverse functions

  1. #1
    Member realintegerz's Avatar
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    Inverse functions

    How do I find f^-1 (2), x for f^-1 (x) = 0

    I have a graph with a function f on it,

    f(x) = [ 2x^3 + 1/2 x + 5 ]/2



    And also, it would be great if someone could find the equation for the inverse of f(x)
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  2. #2
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by realintegerz View Post
    How do I find f^-1 (2), x for f^-1 (x) = 0

    I have a graph with a function f on it,

    f(x) = [ 2x^3 + 1/2 x + 5 ]/2



    And also, it would be great if someone could find the equation for the inverse of f(x)
    Remember that for inverses the domain and range switch. For example

    $\displaystyle f(x)$ has domain A and range B than $\displaystyle f^{-1}(x)$ has domain B and range A

    Ok so using this info we can solve what $\displaystyle f^{-1}(x) = 0$ and $\displaystyle f^{-1}(2)$ is since we know the function is

    $\displaystyle f(x) = \frac{2x^3 +\frac{x}{2} +5}{2}$



    1) $\displaystyle f^{-1}(x) = 0$ is $\displaystyle f(0)=?$

    so

    $\displaystyle x = \frac{5}{2}$



    2)To solve the other problem set

    $\displaystyle 2 = \frac{2x^3 +\frac{x}{2} +5}{2}$

    and solve for x
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  3. #3
    Member realintegerz's Avatar
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    hmmm..

    im stuck on that f^-1 (2)...

    So far i simplified it to...

    -2 = 4x^3 + x
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  4. #4
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by realintegerz View Post
    hmmm..

    im stuck on that f^-1 (2)...

    So far i simplified it to...

    -2 = 4x^3 + x
    i tried using the rational root theorem but couldn't get any nice roots so i used the cubic equation. You could also do it numerically.
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  5. #5
    Member realintegerz's Avatar
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    Quote Originally Posted by 11rdc11 View Post
    i tried using the rational root theorem but couldn't get any nice roots so i used the cubic equation. You could also do it numerically.
    I know the quadratic equation..but not cubic...

    could you explain that?
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