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Math Help - Inverse of function

  1. #1
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    Inverse of function

    Find the inverse of function for f.
    f(x) = \frac{1}{3x-2}

    Its been too long since algebra for me to remember how to properly do this.
    I know how to do the inverse of functions, but I just can't figure out the steps for this one.
    Any help would be much appreciated.
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  2. #2
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by windir View Post
    Find the inverse of function for f.
    f(x) = \frac{1}{3x-2}

    Its been too long since algebra for me to remember how to properly do this.
    I know how to do the inverse of functions, but I just can't figure out the steps for this one.
    Any help would be much appreciated.
    First use y for f(x), it makes it easier to follow.

    y = \frac{1}{3x-2}
    \implies y (3x-2)=1
    \implies 3xy - 2y = 1
    \implies 3xy = 1 +2y

    ... you should be able to continue from there ...
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  3. #3
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    Quote Originally Posted by windir View Post
    Find the inverse of function for f.
    f(x) = \frac{1}{3x-2}

    Its been too long since algebra for me to remember how to properly do this.
    I know how to do the inverse of functions, but I just can't figure out the steps for this one.
    Any help would be much appreciated.
    y = \frac{1}{3x-2}

    swap variables ...

    x = \frac{1}{3y-2}

    solve for y ...

    3y-2 = \frac{1}{x}

    3y = \frac{1}{x} + 2

    y = \frac{1}{3x} + \frac{2}{3} = \frac{1+2x}{3x}
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  4. #4
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    thank you so much.
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