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Thread: Finding the inverse

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by scubasteve94 View Post
    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

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

    $\displaystyle x=\frac{y+2}{1-y}$
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  3. #3
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    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.
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  4. #4
    Senior Member Stroodle's Avatar
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    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 $\displaystyle y$.
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