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  1. #1
    Member CalcGeek31's Avatar
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    Question...

    okay... f(x) = |x|/x

    anyway I am trying to find the domain and range which I am expressing in interval notation...

    I am getting:
    Domain: (-infinity, 0) (0, infinity)
    Range: y is equal to 1 or -1 thats it... how would I express that in interval notation?
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by CalcGeek31 View Post
    okay... f(x) = |x|/x

    anyway I am trying to find the domain and range which I am expressing in interval notation...

    I am getting:
    Domain: (-infinity, 0) (0, infinity)
    Range: y is equal to 1 or -1 thats it... how would I express that in interval notation?
    \begin{aligned} f ~:~ & ]-\infty, ~0[~ \cup ~ ]0, ~+\infty[ & \mapsto & \quad \{-1~,~1\} \\<br />
& \quad \quad \quad \quad x & \mapsto & \quad y \end{aligned}

    It can also been written :

    \begin{aligned} f ~:~ & \mathbb{R}\backslash \{0\} & \mapsto & \quad \{-1~,~1\} \\<br />
& \quad x & \mapsto & \quad y \end{aligned}


    { } usually defines a set of elements.
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  3. #3
    Member CalcGeek31's Avatar
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    I completely understand that... but [-1, 1] means also all numbers in between but that is not true... it can only equal 1 or -1...
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  4. #4
    Moo
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    Quote Originally Posted by CalcGeek31 View Post
    I completely understand that... but [-1, 1] means also all numbers in between but that is not true... it can only equal 1 or -1...
    I wrote {-1,1}, not [-1,1]

    Look carefully ^^
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  5. #5
    Member CalcGeek31's Avatar
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    Ohh... what if Im only using () and [] would it be [-1, -1] [1, 1]?
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  6. #6
    Moo
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    Quote Originally Posted by CalcGeek31 View Post
    Ohh... what if Im only using () and [] would it be [-1, -1] U [1, 1]?
    I guess it would work, but I've never seen this notation

    Or you can write y=f(x)=\left\{\begin{array}{c} -1 \\ 1 \end{array} \right. but it wouldn't really fit in here.
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  7. #7
    Member CalcGeek31's Avatar
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    according to what Ive learned... () is used when the number is not equal to this end... and [] is used when it is equal to either end... EX 2 < x <= 5 would be (2, 5]
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  8. #8
    Moo
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    Quote Originally Posted by CalcGeek31 View Post
    according to what Ive learned... () is used when the number is not equal to this end... and [] is used when it is equal to either end... EX 2 < x <= 5 would be (2, 5]
    I know it, but what I meant is that I've never seen anyone (I'm not saying everybody) using these notations to talk about only one element. We rather use { }
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  9. #9
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    Quote Originally Posted by Moo View Post
    I guess it would work, but I've never seen this notation

    Or you can write y=f(x)=\left\{\begin{array}{c} -1 \\ 1 \end{array} \right. but it wouldn't really fit in here.
    That is set interval notation. You can just write: -1 U 1, but you can still use a set to represent the range: {-1, 1}
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  10. #10
    Member CalcGeek31's Avatar
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    just wondering and thank you by the way... would you happen to help me with my other question?(Question #2...)
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