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How would I go about solving this?

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- Nov 5th 2008, 02:34 PMAskeFinding the Inverse of a Funtion
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How would I go about solving this? - Nov 5th 2008, 03:14 PMLuke774
First make it a "Y=" equation.

Y = x2-5x+6

Switch the Y with the x's

X = Y2-5Y+6

Solve for X

X-6 = Y2-5Y

X-6/5 = Y2

Square root of ((x-6)/5)) = Y

Kind of confusing, but I hope this helps! - Nov 5th 2008, 06:01 PMeuclid2
- Nov 6th 2008, 03:29 AMHallsofIvy
You don't. That is not a "one to one" function and so does not have an inverse. If $\displaystyle f^{-1}(x)$ is the inverse of f(x), then we must have $\displaystyle f^{-1}(f(x))= x$, that is, $\displaystyle f^{-1}$ must 'undo' whatever f does. But f(6)= 0 and f(-1)= 0. $\displaystyle f^{-1}(0)$ can't be both 6 and -1!

Luke774, for some reason, chose to take only the "+" sign on the square root. That's valid but gives the inverse of a slightly different function: $\displaystyle f(x)= x^2- 5x- 6$ with $\displaystyle x\ge 5/2$ and undefined for x< 5/2. Same formula but different domain so different function.