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Math Help - Finding range and function of a specific interval

  1. #1
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    Finding range and function of a specific interval

    Is there an algebraic way to find this if the problem states: Define a function h by h(x)=f(2x) where f is the function defined by f(x)=x^2, with the domain of f in the interval [-1,1].

    a. Find the domain of h
    b. Find the range of h

    How would I find the range of h algebraically without creating a table?
    Last edited by Eraser147; October 4th 2012 at 12:57 PM.
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  2. #2
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    Re: Finding range and function of a specific interval

    Is h(4) defined? No - that would have to be = f(2(4)) = f(8), but f is only defined on [-1,1].
    Is h(2) defined? No - that would have to be = f(2(2)) = f(4), but f is only defined on [-1,1].
    Is h(1) defined? No - that would have to be = f(2(1)) = f(2), but f is only defined on [-1,1].
    Is h(1/2) defined? Yes - that would have to be = f(2(1/2)) = f(1) (= 1), since f IS defined on [-1,1].
    Is h(1/4) defined? Yes - that would have to be = f(2(1/4)) = f(1/2) (= 1/4), since f IS defined on [-1,1].
    Any guesses now what the domain of h might be?
    Once you know the domain of h, how to find the range of h will hopefully become a little clearer.
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  3. #3
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    Re: Finding range and function of a specific interval

    the domain of h is the same as the domain of f, but how do I find the range? Can't I just plug in the intervals?
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  4. #4
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    Re: Finding range and function of a specific interval

    Also, I forgot to state; I have to find the interval of the domain and range.
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  5. #5
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    Re: Finding range and function of a specific interval

    I presume that you are able to calculate directly that h(x)= f(2x)= (2x)^2= 4x^2. And it should not be difficult to see that h has no negative values while h(0)= 0. Further, f(1)= f(-1)= 4 while for any x with |x|< 1, x^2< 1 and so 4x^2< 4
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  6. #6
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    Re: Finding range and function of a specific interval

    My textbook states that the domain interval for h is: [-1/2,1/2] and the range is in the interval [0,1]. Why is this?
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  7. #7
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    Re: Finding range and function of a specific interval

    I mean, the only way that can happen is if -1 = 2x and 1 = 2x
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  8. #8
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    Re: Finding range and function of a specific interval

    Quote Originally Posted by Eraser147 View Post
    My textbook states that the domain interval for h is: [-1/2,1/2] and the range is in the interval [0,1]. Why is this?
    Look at my previous post(#2).
    If you look at the examples, and think about them, I suspect that the reason h's domain is what it is might become clear.
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