Algebra 2 help.

For the function f(x)=(3-4x)^2, find f^-1. Determine whether f^1 is a function.

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asked by Heather

  1. y = (3-4x)^2
    find inverse
    x = (3-4y)^2

    3 -4y = + or - sqrtx
    4 y = 3 + or - sqrt x
    y = (3/4) +/- sqrt x

    this is not a function because there is more than one value of y for eaxh value of x (vertical line rule)

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    posted by Damon

  2. f^-1 is not a function, since f(x) sends two different elements from the domain to the same element of the range.

    f must be 1-to-1 for it to have an inverse. f has two distinct branches:

    y = (3-4x)^2
    3-4x = ±√y
    4x = 3±√y
    x = (3±√y)/4

    So, there is one branch
    f^-1 = (3+√y)/4
    and the other (3-√y)/4
    where y >= 0

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    posted by Steve

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