Find thr inverse of the function with the rule f(x) = (x - 2)/(x + 1)
for this question to I need to change x and y and then solve for y? Any help would be appreciated!!! Thanks
$\displaystyle y=\frac{x-2}{x+1}$ We require a sole x.
$\displaystyle y(x+1)=x-2$
$\displaystyle yx+y=x-2$
$\displaystyle yx-x+y=-2$ With x terms together, they can be factorised
$\displaystyle yx-x=-2-y$
$\displaystyle x(y-1)=-2-y$ there is now a sole x
$\displaystyle x(1-y)=y+2$
$\displaystyle x=\frac{y+2}{1-y}$
Archie Mead solved for x. If your original function was y= f(x), and you want $\displaystyle y= f^{-1}(x)$ you still need to "swap" x and y.
If $\displaystyle y= f(x)= \frac{x- 2}{x+ 1}$, then, after arriving at $\displaystyle x= \frac{y+ 2}{1- y}$, then
$\displaystyle y= f^{-1}(x)= \frac{x+2}{1- x}$.
You could, also, first swap x and y and then solve for y. That will give exactly the same thing.