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Investigating Properties of Inverse Functions

  1. Apr 7, 2006 #1
    Ok here is teh question, there is parts a-e, i have a-d answered correctly, but am having trouble on e.

    Q: A function g is g(x)=4(x-3)^2 + 1

    a) Graph g and the inverse of g. (Already completed)

    b) At what points do g and the inverse of g intersect. (completed)

    c) Determine an equation that defines the inverse of g.
    the answer is y=3 +/- (root of (x-1/4) )

    d) State restrictions on the domain or range of g so that its inverse is a function.

    i got x is greater or equal to 3 and x is less than or equal to 3

    then finally

    e) Suppose teh domain of g is {x|2 < or equal to x < or equal to 5, XER}
    Would the inverse be a function? Justify your answer.

    Ok. The answers say the inverse is not a function because the

    inverse of g (5) = 2 and
    inverse of g (5) =4

    i guess that makes sense because there is two y coordinates for that x. My question how do you algabraically solve that. Help would be appreciated. Thanks
  2. jcsd
  3. Apr 8, 2006 #2
    Simple. Hopefully your inverse function was supposed to be:
    [tex]y=3 \pm \sqrt{\frac{x-1}{4}}[/tex]

    So using the + sign: y(5) = 3 + 1 = 4.
    Using the - sign: y(5) = 3 -1 = 2.

    Since we may use either sign, that means that y(5) is double valued, which violates the definition of a function.

    Last edited: Apr 8, 2006
  4. Apr 8, 2006 #3

    Thanks alot Dan.

    One question. Why are you using f(5). Why did you chose the number 5. Is it because it is the highest possible x coordinate.

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