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Thread: find inverse function

  1. #1
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    find inverse function

    $\displaystyle f(x) = 5(x-2)^3 - 6$

    Could someone help me find the inverse function for this function?

    I understand these steps:

    Set f(x) to y
    $\displaystyle y = 5(x-2)^3 - 6$

    Swap x and y
    $\displaystyle x = 5(y-2)^3 - 6$

    I think I'm supposed to solve for Y, but I'm not sure how to continue.
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  2. #2
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    Quote Originally Posted by absvalue View Post
    $\displaystyle f(x) = 5(x-2)^3 - 6$

    Could someone help me find the inverse function for this function?

    I understand these steps:

    Set f(x) to y
    $\displaystyle y = 5(x-2)^3 - 6$

    Swap x and y
    $\displaystyle x = 5(y-2)^3 - 6$

    I think I'm supposed to solve for Y, but I'm not sure how to continue.
    $\displaystyle x = 5(y-2)^3 - 6$

    add 6 to both sides ...

    $\displaystyle
    x+6 = 5(y-2)^3
    $

    divide both sides by 5 ...

    $\displaystyle
    \frac{x+6}{5} = (y-2)^3
    $

    take the cube root of both sides ...

    $\displaystyle
    \sqrt[3]{\frac{x+6}{5}} = y-2
    $

    add 2 to both sides ...

    $\displaystyle
    \sqrt[3]{\frac{x+6}{5}} + 2 = y
    $

    you're done.
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  3. #3
    Member
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    $\displaystyle x = 5(y-2)^3 - 6$

    So far you are right. Like you said, you need to solve for y, and you just need some basic algebra to do that.

    $\displaystyle x + 6 = 5(y-2)^3$
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  4. #4
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    Smile

    hi
    $\displaystyle (y-2)^{3}=\frac{x+6}{5}\Leftrightarrow y-2=\sqrt[3]{\frac{x+6}{5}}\Leftrightarrow y= \sqrt[3]{\frac{x+6}{5}}+2$,now change $\displaystyle y$ to $\displaystyle f^{-1}(x)$
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