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!