Finding Inverse of Functions

Here's what I have:

f(x)=$\displaystyle \frac{x+3}{x+4}$; x not equal to -4

$\displaystyle f^-1(x)=\frac{3-4x}{x-1}$; x not equal to -1

$\displaystyle f(x): y=\frac{x+3}{x+4}$

$\displaystyle x=\frac{y+3}{y+4}$

$\displaystyle x(y+4)=y+3$

$\displaystyle xy +4x=y+3$

$\displaystyle xy=y-1$

And that's pretty much it for me. I wish I could copy and paste the graph but looking at it it seems that I might just be able to read the graph or take the zeros of all the x's and simply construct the lines of the graph based on that, thereby avoiding the algebra. I have a feeling that's just wishful thinking though. Any and all help is greatly appreciated. Thanks. (Bow)

Re: Finding Inverse of Functions

Hello, Ingersoll!

I'll try to clarify what you wrote . . .

Quote:

$\displaystyle \text{Find the inverse of: }\:f(x) \:=\: \frac{x+3}{x+4}\quad x \ne -4$

$\displaystyle \text{Answer: }\:f^{\text{-}1}(x)\:=\:\frac{3-4x}{x-1}\quad x \ne 1$

$\displaystyle y \;=\;\frac{x+3}{x+4}$

$\displaystyle x \;=\;\frac{y+3}{y+4}$

$\displaystyle x(y+4)\;=\;y+3$

$\displaystyle xy +4x\;=\;y+3$

$\displaystyle xy\;=\;y-1$ . What?

You had: -- $\displaystyle xy +4x \;=\;y + 3$

Rearrange: .$\displaystyle xy - y \;=\;3 - 4x$

Factor:a---$\displaystyle (x-1)y \;=\;3-4x$

Therefore: - - . . . $\displaystyle y \;=\;\frac{3-4x}{x-1}$