# Find the inverse domain and range of f(x)?

• Apr 9th 2010, 03:23 PM
sydewayzlocc
Find the inverse domain and range of f(x)?
I am stuck trying to find the inverse of f(x)=x+6/x, can someone help?
• Apr 9th 2010, 03:30 PM
skeeter
Quote:

Originally Posted by sydewayzlocc
I am stuck trying to find the inverse of f(x)=x+6/x, can someone help?

$\displaystyle f(x) = \frac{x+6}{x}$ or $\displaystyle x + \frac{6}{x}$ ?

• Apr 9th 2010, 03:32 PM
sydewayzlocc
i apologize it was (x+6)/(x)
• Apr 9th 2010, 03:39 PM
macosxnerd101
To find the inverse of a function, substitute y for every x, then x for y's. So your function would then look like: x = (y+6)/y. Now just solve for y, and you have your inverse function.
• Apr 9th 2010, 03:42 PM
skeeter
Quote:

Originally Posted by sydewayzlocc
... it was (x+6)/(x)

$\displaystyle y = \frac{x+6}{x}$

swap variables ...

$\displaystyle x = \frac{y+6}{y}$

solve for $\displaystyle y$ ...

$\displaystyle xy = y+6$

$\displaystyle xy - y = 6$

$\displaystyle y(x-1) = 6$

$\displaystyle y = \frac{6}{x-1}$