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Math Help - determine the constants such that f = f^-1

  1. #1
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    determine the constants such that f = f^-1

    f(x) = (ax+b)/(cx+d)

    Find the constants that f is equal to its inverse. I initially claimed that a=d and c=b for this to be true. My professor claims that is not true. He gave the hint that you have to take the inverse and this substitute it into f(x) which should equal x. For the inverse I get (xd-b)/(a-cx) which I do not believe it is right. However, I do not know how to isolate for x to substitute it back into f(x) so it will be "proof" that the constants are true. For his way I got the constants to be a=d and b and c must be negatives. Any hints?
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  2. #2
    MHF Contributor Amer's Avatar
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    Re: determine the constants such that f = f^-1

    f = (ax+b)/(cx+d)

    f^-1 = (xd-b)/(a-cx)

    try
    b = 0 , a=-d , c arbitrary

    f= (-dx )/(cx + d)

    f^-1 = (xd)/( -d - cx) = -dx/ (cx+d) = f ends
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