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Math Help - 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
    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}
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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 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.
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  4. #4
    Senior Member Stroodle's Avatar
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    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.
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