Question

inverse of f(x)=(x+1)/(2x+1) I know how to get the inverse if the bottom or top of the fraction have an x on their own, but i am not sure how to move y over when x is on both top and bottom, help please and thanks guys :D

Answer 1

To solve for the inverse
1. replace f(x) with y
2. switch all x with y and y with x
3. solve for y
4. replace y with $f^{-1}(x)$



$f(x)=\frac{x+1}{2x+1}$
replace
$y=\frac{x+1}{2x+1}$
switch
$x=\frac{y+1}{2y+1}$
solve
$(2y+1)(x)=y+1$
$2yx+x=y+1 [tex]x-1=y-2xy$
$x-1=y(1-2x)$
$\frac{x-1}{1-2x}=y$
$y=\frac{x-1}{1-2x}$
replace
$f^{-1}(x)=\frac{x-1}{1-2x}$