# Inverse Functions

• Jan 10th 2008, 02:00 PM
Macleef
Inverse Functions
Find the inverses of the following functions.

i) $\displaystyle y = \frac {4x - 1}{3x + 2}$

$\displaystyle x = \frac {4 - 1}{3y + 2}$

$\displaystyle x(3y + 2) = 4y - 1$

$\displaystyle x(3y + 2) + 1 = 4y$

$\displaystyle 3xy + 2x + 1 = 4y$

$\displaystyle \frac {3xy + 2x + 1}{4} = y$

$\displaystyle 2x + 1 = y - \frac {3xy}{4}$

This is how far I got. . .and I don't know what to do now. . .
• Jan 10th 2008, 02:06 PM
Jhevon
Quote:

Originally Posted by Macleef
Find the inverses of the following functions.

i) $\displaystyle y = \frac {4x - 1}{3x + 2}$

$\displaystyle x = \frac {4 - 1}{3y + 2}$

$\displaystyle x(3y + 2) = 4y - 1$

$\displaystyle x(3y + 2) + 1 = 4y$

$\displaystyle 3xy + 2x + 1 = 4y$

$\displaystyle \color{red}\frac {3xy + 2x + 1}{4} = y$

$\displaystyle 2x + 1 = y - \frac {3xy}{4}$

This is how far I got. . .and I don't know what to do now. . .

your mistake occurred on the line in red. you should have, instead, get all terms with y in them on one side and factor out the y, then divide through by the thing you have multiplying y. though, you could still do it in your last line. it will be messier than it has to be though
• Jan 10th 2008, 02:14 PM
Macleef
Quote:

Originally Posted by Jhevon
your mistake occurred on the line in red. you should have, instead, get all terms with y in them on one side and factor out the y, then divide through by the thing you have multiplying y. though, you could still do it in your last line. it will be messier than it has to be though

Could you please show me how?

I did what you said and got the following. . .

$\displaystyle 2x + 1 = 4y - 3xy$

And now. . .I don't know what to do. . .I don't know how to isolate for the variable with two terms that aren't the same on one side. . .
• Jan 10th 2008, 02:18 PM
Jhevon
Quote:

Originally Posted by Macleef
Could you please show me how?

I did what you said and got the following. . .

$\displaystyle 2x + 1 = 4y - 3xy$

And now. . .I don't know what to do. . .I don't know how to isolate for the variable with two terms that aren't the same on one side. . .

i said factor out the y

so we get $\displaystyle 2x + 1 = y(4 - 3x)$

now divide by 4 - 3x

$\displaystyle \Rightarrow y = \frac {2x + 1}{4 - 3x}$