Inverse of function

• Oct 1st 2009, 01:24 PM
windir
Inverse of function
Find the inverse of function for $\displaystyle f.$
$\displaystyle f(x) = \frac{1}{3x-2}$

Its been too long since algebra for me to remember how to properly do this.
I know how to do the inverse of functions, but I just can't figure out the steps for this one.
Any help would be much appreciated.
• Oct 1st 2009, 01:31 PM
Matt Westwood
Quote:

Originally Posted by windir
Find the inverse of function for $\displaystyle f.$
$\displaystyle f(x) = \frac{1}{3x-2}$

Its been too long since algebra for me to remember how to properly do this.
I know how to do the inverse of functions, but I just can't figure out the steps for this one.
Any help would be much appreciated.

First use y for f(x), it makes it easier to follow.

$\displaystyle y = \frac{1}{3x-2}$
$\displaystyle \implies y (3x-2)=1$
$\displaystyle \implies 3xy - 2y = 1$
$\displaystyle \implies 3xy = 1 +2y$

... you should be able to continue from there ...
• Oct 1st 2009, 01:31 PM
skeeter
Quote:

Originally Posted by windir
Find the inverse of function for $\displaystyle f.$
$\displaystyle f(x) = \frac{1}{3x-2}$

Its been too long since algebra for me to remember how to properly do this.
I know how to do the inverse of functions, but I just can't figure out the steps for this one.
Any help would be much appreciated.

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

swap variables ...

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

solve for y ...

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

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

$\displaystyle y = \frac{1}{3x} + \frac{2}{3} = \frac{1+2x}{3x}$
• Oct 1st 2009, 01:53 PM
windir
thank you so much.