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Math Help - A little help sir

  1. #1
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    A little help sir

    Q. If the domain of the fxn y=5+3x is the set {x: 1 ≤ x ≤ 4} find the range of the fxn and express it as a set..
    Last edited by CaptainBlack; July 16th 2008 at 09:59 AM.
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  2. #2
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    Quote Originally Posted by ranthrave View Post
    Q. If the domain of the fxn y=5+3x is the set {x: 1 ≤ x ≤ 4} find the range of the fxn and express it as a set..
    1 \leq x \leq 4 \Rightarrow 3 \leq 3x \leq 12 \Rightarrow 8 \leq 5+3x \leq 17

    So the range is the set \{y: 8 \leq y \leq 17\}
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by ranthrave View Post
    Q. If the domain of the fxn y=5+3x is the set {x: 1 ≤ x ≤ 4} find the range of the fxn and express it as a set..
    Alternatively notice that f(x) is increasing \forall{x}\in\mathbb{R}

    Therefore we should have that x_0<x_1\Rightarrow{f(x_0)<f(x_1)}

    So the maximum on this interval should be f(\text{smallest x-value}) and the largest f(\text{largest x-value})

    So

    f(1)\leq{y}\leq{f(4)}\Rightarrow{8\leq{y}\leq{17}}
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