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Math Help - Domain Of Functions

  1. #1
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    Domain Of Functions

    Hello Everybody ,

    I am working on some exercises here , about the domains of some given functions , but my solutions differ than the book ones... Am i wrong in something or the book has indeed mistakes ???


    Asks for the domain of the function : f(x) = logx4

    The solution it gives me is : D(f) = (0,1)u(1,-oo).

    Firstly , why (1,-oo)? i think it's obviously a mistake , what's your opinion?

    Also , do i really need (0,1) wouldn't it be better if i only had D(f) = (1,+oo) ?


    Thaks in advance for your answers !!!
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  2. #2
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    Quote Originally Posted by Homo-Sapiens View Post
    Hello Everybody ,

    I am working on some exercises here , about the domains of some given functions , but my solutions differ than the book ones... Am i wrong in something or the book has indeed mistakes ???


    Asks for the domain of the function : f(x) = logx4

    The solution it gives me is : D(f) = (0,1)u(1,-oo).

    Firstly , why (1,-oo)? i think it's obviously a mistake , what's your opinion?

    Also , do i really need (0,1) wouldn't it be better if i only had D(f) = (1,+oo) ?


    Thaks in advance for your answers !!!
    f(x) = \log_x(4)

    x is the base of the logarithm ... the base of a log can be any positive value other than 1

    x \in (0,1) \cup (1,\infty)<br />

    in my opinion, it's a typo.
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  3. #3
    Super Member Bacterius's Avatar
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    Reply

    There are a lot of typo's then, since :
    - intervals are written with square brackets for real intervals, and braces for integer intervals, but never round brackets.
    - infinities are conventionally always excluded from intervals.
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  4. #4
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    Quote Originally Posted by Bacterius View Post
    There are a lot of typo's then, since :
    - intervals are written with square brackets for real intervals, and braces for integer intervals, but never round brackets.
    Definitely not...

     [-1,1] = \{x \in \mathbb{R} : -1 \leq x \leq 1\}
    While
    (-1,1] = \{x \in \mathbb{R} : -1 < x \leq 1\}
    And
    (-1,1) =\{x \in \mathbb{R} : -1 < x < 1\}

    That is, square brackets indicate inclusion of the end point, while round brackets do not.

    - infinities are conventionally always excluded from intervals.
    This is also incorrect. The notation (a,\infty ), (-\infty, \infty ), (-\infty, b] is very commonly used.

    Skeeter is correct, I believe... there seems to be a typo. Also,

    Also , do i really need (0,1) wouldn't it be better if i only had D(f) = (1,+oo) ?
    This is not a question of need... It is a question of "can I substitute these values of x to the equation such that it would still hold?"
    In this case (for the interval (0,1)), the answer is yes, so it must be included in the answer.
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  5. #5
    Super Member Bacterius's Avatar
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    Then conventions are not exactly "conventions". From where I come (France), we write :

    4 < x <= 5 -> x C ]4; 5]

    (C is "belongs to", but I have to read this tex tutorial)

    And : 3 <= x -> x C [3; +inf[
    And : x > 9 -> x C ]-inf; 9[
    And for R -> ]-inf; +inf[

    Of course, "inf" is the rotated 8, but again the tex tutorial is waiting for me.

    I guess the exclude bracket (]-inf) is equivalent to your round bracket ((inf), is that right ? If so then mea culpa, I don't know all math writing in english countries yet since I just moved some weeks ago. I'm only willing to learn but this is going to take some time though.
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  6. #6
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  7. #7
    Super Member Bacterius's Avatar
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    In which countries does this notation apply ? (just to know)
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