college alg

the function f(x)=6x+9/3x-7

find the inverse and check answer

f^-1(x)=?

please show work

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  1. I have a strong feeling you meant
    f(x) = (6x+9)/(3x-7)

    if so, let
    y = (6x+9)/(3x-7)
    inverse:
    x = (6y+9)/(3y-7)

    solving that for y ....

    3xy - 7x = 6y+9
    3xy - 6y = 7x+9
    y(3x - 6) = 7x+9
    y = (7x+9)/(3x-6)

    f^-1 (x) = (7x+9)/(3x-6)

    check:
    f(0) = 9/-7
    f^-1(-9/7) = (7(-9/7) + 9)/(3(-9/7)-6)
    = 0/...
    = 0

    (This does not prove that my answer is correct, but shows a very strong probability that it is correct)

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