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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

Respuesta :

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 [tex]f^{-1}(x)[/tex]



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

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