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

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

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

3. 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.

4. Another way to do it is:

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

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

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

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