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20 October, 22:15

For which function is f (x) equal to f^-1 (x) ?

f (x) = x+6x-6

f (x) = x+2/x-2

f (x) = x+1/x-1

f (x) = x+5/x-5

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  1. 20 October, 23:28
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    We will find the inverse of the given functions:

    y = x + 2 / x-2

    (x-2) y = x + 2

    -2y + xy = x + 2

    -2y + xy = x + 2

    x (y - 1) = 2 + 2y

    x (y - 1) = 2 (y + 1)

    x = 2 (y + 1) / (y - 1)

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

    The inverse is different.

    f (x) = x + 1 / x-1

    y = x + 1 / x-1

    (x-1) y = x + 1

    -y + xy = x + 1

    x (y - 1) = 1 + y

    x (y - 1) = (y + 1)

    x = (y + 1) / (y - 1)

    f (x) ^ - 1 = (x + 1) / (x - 1)

    The inverse is the same.

    Answer:

    f (x) = x + 1 / x-1

    f (x) ^ - 1 = (x + 1) / (x - 1)

    f (x) = f (x) ^ - 1
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