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Mathematics 27 Online
OpenStudy (anonymous):

help!

OpenStudy (anonymous):

OpenStudy (anonymous):

@amistre64

OpenStudy (amistre64):

essentially, an inverse function swaps xs and ys

OpenStudy (amistre64):

let y = f(x); and solve x = f(y) for y

OpenStudy (amistre64):

might want to "complete the square" first tho

OpenStudy (amistre64):

\[x = y^2 + yx\] \[x+\frac{b^2}{4} = x^2 + bx+\frac{b^2}{4}\] \[x+\frac{b^2}{4} = (y+\frac b2)^2\] \[\sqrt{x+\frac{b^2}{4}} = y+\frac b2\] \[\sqrt{x+\frac{b^2}{4}} -\frac b2= y\]

OpenStudy (dmnts):

\[x=\frac{ -9+\sqrt{81+4y} }{ 2 }\]

OpenStudy (dmnts):

just switch x and y

OpenStudy (anonymous):

@amistre64 yeah i figured you would have to square but was not sure. thanks!

OpenStudy (amistre64):

my latex got a little messed up :)

OpenStudy (amistre64):

DM went ahead and solved for "x", which is fine as well

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