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Math Help - variable in denominator

  1. #1
    Member sinewave85's Avatar
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    variable in denominator

    I can't remember how to work with functions\equations where there is a variable in the denominator, like

    <br />
f(x)=\frac {ax+b}{cx +d}  \  \mbox {or}  \  y=\frac {ax+b}{cx +d}         <br />

    specificly, how to get the inverse function after you swap the x and y, but in general just how to get the variable out of the denominator. I know you multiply by an expression equivalent to 1, but I can't remember how. This is driving me nuts. Thanks.
    Last edited by sinewave85; October 10th 2007 at 03:04 PM.
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  2. #2
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    Hello, sinewave85!

    Hope this refreshes your memory . . .


    Find the inverse of: . y\:=\:\frac {ax+b}{cx +d}
    Swap the variables: . x \:=\:\frac{ay+b}{cy+d}

    Multiply by (cy+d)\!:\;\;x(cy+d) \:=\:ay+b

    Expand: . cxy + dx \:=\:ay + b

    Rearrange terms: . cxy - ay \:=\:b - dx

    Factor: . y(cx - a) \:=\:b - dx

    Hence: . y \:=\:\frac{b-dx}{cx-a}

    . . Therefore: . f^{-1}(x)\:=\:\frac{b-dx}{cx-a}

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  3. #3
    Member sinewave85's Avatar
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    That helps! I don't know what I was thinking.
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