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Thread: More Inverse...

  1. #1
    Newbie Pre Lives's Avatar
    Dec 2008

    More Inverse...

    I'm sorry I have to keep pestering everyone about inverse. I ran into a problem on my homework that is frustrating me. I still kind of don't get it.... If anyone could put it put it step by step it would be greatly appreciated.

    Find the Inverse: y= 2x^2 + 6x - 4
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  2. #2
    Junior Member
    Nov 2008
    To do this you need to isolate x then switch y for x and vice versa. So let's isolate x:

    $\displaystyle y=2x^2+6x-4$

    $\displaystyle y=2(x^2+3x)-4$

    $\displaystyle y=2(x^2+3x+\frac{9}{4}-\frac{9}{4})-4$ (complete the square: 3 divided by 2 squared)

    $\displaystyle y=2(x+\frac{3}{2})^2-\frac{9}{2}-4$

    $\displaystyle y=2(x+\frac{3}{2})^2-\frac{17}{2}$

    $\displaystyle \frac{1}{2}(y+\frac{17}{2})=(x+\frac{3}{2})^2$

    $\displaystyle x=\sqrt{\frac{1}{2}(y+\frac{17}{2})}-\frac{3}{2}$

    So then the inverse of y is $\displaystyle y^{-1}(x)=\sqrt{\frac{1}{2}(x+\frac{17}{2})}-\frac{3}{2}$
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