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7. Determine the inverse of each relation given.

a. f(x) = 1/x-2 + 3


b. f(x) = 2(x – 4)^2 + 5

  • math -

    y = 1/(x-2) + 3
    y-3 = 1/(x-2)
    x-2 = 1/(y-3)
    x = 1/(y-3) + 2

    so, f-1(x) = 1/(x-3) + 2

    y = 2(x-4)^2 + 5
    y-5 = 2(x-4)^2
    (y-5)/2 = (x-4)^2
    now, we can use ± root, so let's choose the + root:
    √[(y-5)/2] = x-4
    √[(y-5)/2]+4 = x

    so, f-1(x) = √[(x-5)/2] + 4

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