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 Post subject: Finding the Inverse of a Quadratic Function?Posted: Wed, 13 Jun 2012 09:39:21 UTC
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Joined: Wed, 13 Jun 2012 09:29:08 UTC
Posts: 2
Hi, need some help in the aspect of finding the inverse of a quadratic function. I know how to solve simple ones, but what happens when the quadratic function is in the form of a fraction

f(x) = (x^2 - x + 1) / (x^2 + x + 1)

So far I have only gotten this far:
y = (x^2 - x + 1) / (x^2 + x + 1)
yx^2 + yx + y = x^2 - x + 1
(y-1)x^2 + (y+1)x + (y-1) = 0
(y-1)(x^2 +1) + (y+1)x = 0

Thanks in advance!

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 Post subject: Re: Finding the Inverse of a Quadratic Function?Posted: Wed, 13 Jun 2012 12:13:31 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 23 Feb 2009 23:20:33 UTC
Posts: 1049
Location: Adelaide, Australia
cyh96 wrote:
Hi, need some help in the aspect of finding the inverse of a quadratic function. I know how to solve simple ones, but what happens when the quadratic function is in the form of a fraction

f(x) = (x^2 - x + 1) / (x^2 + x + 1)

So far I have only gotten this far:
y = (x^2 - x + 1) / (x^2 + x + 1)
yx^2 + yx + y = x^2 - x + 1
(y-1)x^2 + (y+1)x + (y-1) = 0
(y-1)(x^2 +1) + (y+1)x = 0

Thanks in advance!

Notice that because f(x) is not a one-to-one function, there are zero, one, or two solutions for a given y, so there is no single inverse function.

This is a quadratic equation in x, and now you can apply the quadratic formula.

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 Post subject: Re: Finding the Inverse of a Quadratic Function?Posted: Wed, 13 Jun 2012 15:28:44 UTC
 S.O.S. Newbie

Joined: Wed, 13 Jun 2012 09:29:08 UTC
Posts: 2
So is it safe to say that there is no inverse function for all quadratic eqns?
Thanks

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 Post subject: Re: Finding the Inverse of a Quadratic Function?Posted: Wed, 13 Jun 2012 15:42:40 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6007
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
cyh96 wrote:
So is it safe to say that there is no inverse function for all quadratic eqns?
Thanks

No.

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 Post subject: Re: Finding the Inverse of a Quadratic Function?Posted: Wed, 13 Jun 2012 15:50:22 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7949
Location: Lexington, MA
Hello, cyh96!

Quote:

So far I have only gotten this far:

. .

. .

. .

. . . . . . keep going

. .

. . . . . a quadratic in

Quadratic Formula: .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . . . .

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 Post subject: Re: Finding the Inverse of a Quadratic Function?Posted: Wed, 13 Jun 2012 15:57:58 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12098
Location: Austin, TX
This function is NOT 1-1, so it does not have an inverse. Take for example the image point 0, what is is it or is it ?

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 Post subject: Re: Finding the Inverse of a Quadratic Function?Posted: Wed, 13 Jun 2012 16:01:36 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12098
Location: Austin, TX
cyh96 wrote:
So is it safe to say that there is no inverse function for all quadratic eqns?
Thanks

What do you mean by "inverse function for an equation"?

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