math

f(x) =x-2/x-3. I calculated f^-1 (x)to be 3x-2/y-1. How do I use f^-1 (x) to evaluate (x-2/x-3)=4.

P.S/ f^-1 means 'f' inverse.

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  1. First of all, I am sure you meant
    f(x) = (x-2)/(x-3) , those brackets are essential!
    or
    y = (x-2)/(x-3)

    step1 in forming the inverse:
    switch the x and y variables
    ---> x = (y-2)/(y-3)
    step2: solve this new equation for y

    xy - 3x = y-2
    xy - y = 3x - 2
    y(x-1) = 3x-2
    y = (3x-2)/(x-1) , notice the brackets again ?
    (you had y-1 in the denominator , I hope it was just a typo )

    f^-1 (x) = (3x-2)/(x-1)

    I don't understand what you mean by
    "How do I use f^-1 (x) to evaluate (x-2/x-3)=4"

    did you mean evaluate
    f( (x-2)/(x-3) ) ??
    or
    are you solving (x-2)/(x-3) = 4 ??

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