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Math Help - find inverse function

  1. #1
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    find inverse function

    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
    y = 5(x-2)^3 - 6

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

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

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

    add 6 to both sides ...

     <br />
x+6 = 5(y-2)^3<br />

    divide both sides by 5 ...

     <br />
\frac{x+6}{5} = (y-2)^3<br />

    take the cube root of both sides ...

     <br />
\sqrt[3]{\frac{x+6}{5}} = y-2<br />

    add 2 to both sides ...

     <br />
\sqrt[3]{\frac{x+6}{5}} + 2 = y<br />

    you're done.
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  3. #3
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    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.

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

    hi
    (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 y to f^{-1}(x)
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