1. ## Finding the inverse

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

2. Originally Posted by scubasteve94
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
$y=\frac{x-2}{x+1}$ We require a sole x.

$y(x+1)=x-2$

$yx+y=x-2$

$yx-x+y=-2$ With x terms together, they can be factorised

$yx-x=-2-y$

$x(y-1)=-2-y$ there is now a sole x

$x(1-y)=y+2$

$x=\frac{y+2}{1-y}$

3. Archie Mead solved for x. If your original function was y= f(x), and you want $y= f^{-1}(x)$ you still need to "swap" x and y.

If $y= f(x)= \frac{x- 2}{x+ 1}$, then, after arriving at $x= \frac{y+ 2}{1- y}$, then
$y= f^{-1}(x)= \frac{x+2}{1- x}$.

You could, also, first swap x and y and then solve for y. That will give exactly the same thing.

4. Another way to do it is:

$y=\frac{x-2}{x+1}$

$y=\frac{(x+1)-3}{(x+1)}$

$y=1-\frac{3}{x+1}$

Then swap $x$ and $y$, and solve for $y$.