How do you find the inverse of $y=2x^(2)-12x$ ?

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Answer 1 · 2016-04-19T01:14:17

The inverse of a function can be found algebraically by switching the x and y value, and isolating y.

Now, to find the inverse of a quadratic, it's easier to complete the square to convert to vertex form.

$y = 2(x^2 - 6x + m)$

$m = (b/2)^2$

$m = (-6/2)^2$

$m = 9$

$y = 2(x^2 - 6x + 9 - 9)$

$y = 2(x^2 - 6x + 9) - 18$

$y = 2(x - 3)^2 - 18$

$x = 2(y - 3)^2 - 18$

$x + 18 = 2(y - 3)^2$

$(x + 18)/2 = (y - 3)^2$

$+-sqrt(1/2x + 9) = y - 3$

$+-sqrt(1/2x + 9) + 3 = y$

Thus, $ƒ^-1(x) = +-sqrt(1/2x + 9) + 3$ . Don't forget the $f^-1(x)$ notation; I've been docked marks for this before.

Hopefully this helps!

How do you find the inverse of y=2x^(2)-12xy=2x^(2)-12x?