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precalc

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How would you find the inverse of these two functions: f(x)=4/(x-4)^2 and
f(x)=x^2-8x+16

could you please show me step by step i have been trying to figure it out for hours.

  • precalc - ,

    first one:
    y = 4/(x-4)^2
    inverse is
    x = 4/(y-4)^2
    solving this for y .....
    (y-4)^2 = 4/x
    y - 4 = ± 2/√x
    y = 4 ± 2/√x

    2nd .....
    inverse is
    x = y^2 - 8y + 16
    y^2 - 8y + 16 - x = 0
    use the quadratic equation
    where a=1, b=-8 and c = 16-x to solve for y

  • precalc - ,

    thanks i got the first one now!

    for the second one I used the quadratic eqn and got 4 but that is not the answer?

  • precalc - ,

    y = (8 ± √(64-4(1)(16-x))/2
    = (8 ± √(4x) )/2
    = (8 ± 2√x)/2
    = 4 ± √x

    check: let x = 3 into the first
    y = 9 - 24 + 16 = 1

    put x = 1 into the second:
    y = 4 ± √1 = 5 or 3

    notice the the inverse of each of the equations is not a function.

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