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Math Help - Inverse Functions

  1. #1
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    Inverse Functions

    Find the inverses of the following functions.

    i) y = \frac {4x - 1}{3x + 2}

    x = \frac {4 - 1}{3y + 2}

    x(3y + 2) = 4y - 1

    x(3y + 2) + 1 = 4y

    3xy + 2x + 1 = 4y

    \frac {3xy + 2x + 1}{4} = y

    2x + 1 = y - \frac {3xy}{4}

    This is how far I got. . .and I don't know what to do now. . .
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Macleef View Post
    Find the inverses of the following functions.

    i) y = \frac {4x - 1}{3x + 2}

    x = \frac {4 - 1}{3y + 2}

    x(3y + 2) = 4y - 1

    x(3y + 2) + 1 = 4y

    3xy + 2x + 1 = 4y

    \color{red}\frac {3xy + 2x + 1}{4} = y

    2x + 1 = y - \frac {3xy}{4}

    This is how far I got. . .and I don't know what to do now. . .
    your mistake occurred on the line in red. you should have, instead, get all terms with y in them on one side and factor out the y, then divide through by the thing you have multiplying y. though, you could still do it in your last line. it will be messier than it has to be though
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    your mistake occurred on the line in red. you should have, instead, get all terms with y in them on one side and factor out the y, then divide through by the thing you have multiplying y. though, you could still do it in your last line. it will be messier than it has to be though
    Could you please show me how?

    I did what you said and got the following. . .

    2x + 1 = 4y - 3xy

    And now. . .I don't know what to do. . .I don't know how to isolate for the variable with two terms that aren't the same on one side. . .
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Macleef View Post
    Could you please show me how?

    I did what you said and got the following. . .

    2x + 1 = 4y - 3xy

    And now. . .I don't know what to do. . .I don't know how to isolate for the variable with two terms that aren't the same on one side. . .
    i said factor out the y

    so we get 2x + 1 = y(4 - 3x)

    now divide by 4 - 3x

    \Rightarrow y = \frac {2x + 1}{4 - 3x}
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