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    how do you find the inverse of f(x) = x+2 / x-5 and state its domain

    :confused:

    thankkkkks
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    y = \frac{x+2}{x-5}

    Change x to y and vice versa.

    Rearrange to make y the subject.
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    Let y=\dfrac{x+2}{x-5} and then rearrange to make x the subject (start by multiplying through by x-5). Then you have x=f^{-1}(y), so relabelling x \leftrightarrow y gives you f^{-1}(x).

    To state its domain, think about the value(s) that the function can't take. Then the domain is everything except this/these value/values.
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    (Original post by Mr M)
    y = \frac{x+2}{x-5}

    Change x to y and vice versa.

    Rearrange to make y the subject.
    thankkks

    the rearranging is the part i get stuck on..

    my working out:

    x = y+2 / y-5

    x(y-5) = y+2

    xy - 5x = y + 2

    y = xy - 5x + 2

    but surely this is wrong because there is still a y? :confused:
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    y-xy = y(1-x)
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    boromir (borrow me ear) has the correct approach.
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    (Original post by Mr M)
    boromir (borrow me ear) has the correct approach.
    Totally not fair dude, I can't do anything like that with your name, it's like you knew that :p: well, what goes comes around
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    (Original post by boromir9111)
    y-xy = y(1-x)
    how do you get that?!

    i can get the LHS but not the RHS? :/

    thanks
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    How about multiplying both sides by (x-5) - that will remove the deonominator on the right hand side, then you get

    y(x-5) = x + 2
    yx - 5y = x + 2
    take the x over to the other side, take the right over to the side the x came from and then
    yx - x = 5y + 2
    factorise
    x(y-1) = 5y + 2
    then divide by (y-1)
    x = 5y+2 / y-1

    so the inverse therefore would be 5x+2 / x-1.

    The domain is the range of values that x can take. If you want to find that then look at the denominator on the inverse
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    (Original post by boomboompow.)
    how do you get that?!

    i can get the LHS but not the RHS? :/

    thanks
    expand out y(1-x) and you will see that it expands out to y-xy post here again if you don't understand that or anything else
 
 
 
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