If f= x+1/x+3 , find g, it's inverse, if it exists.
Thanks in advance!
Finding the Inverse of a Function
This site gives a good explanation.
$\displaystyle y=\frac {x+1}{x+3}$
Solve for x:
$\displaystyle y(x+3)=x+1$
$\displaystyle
yx+3y=x+1$
$\displaystyle 3y-1=x-yx$
$\displaystyle 3y-1=x(1-y)$
$\displaystyle x=\frac {3y-1}{1-y}$
Now switch the x and y:
$\displaystyle y = \frac {3x-1}{1-x}$
And y is your inverse.
for these inverse problems, simply switch all x's with y's and all y's with x's. Note that for f(x), just consider it to mean y. Ok, so you switched the x's and y's. Now solve for y. That's it.
-Andy
Edit: And I almost forgot, check your restriction(s). Only God can divide by zero.