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Math Help - Domain and Range

  1. #1
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    Question Domain and Range

    Hello mates, I need help with this,

    Assume that:

    f(x) =   \sqrt \frac{x-1}{x+1}

    a. Find the domain of f
    b. If f(a) = 2, find f(a), f(a), f (1/a), and 1/f(a).
    c. Give an example of a function whose domain equals (1, 1) and whose range equals the range of f.
    d. Sketch the graph of a function whose domain equals the domain of f and whose range equals {1, 1}.
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  2. #2
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    Quote Originally Posted by OVechkin8 View Post
    Hello mates, I need help with this,

    Assume that:

    f(x) =  \sqrt \frac{x-1}{x+1}

    a. Find the domain of f
    b. If f(a) = 2, find f(a), f(a), f (1/a), and 1/f(a).
    c. Give an example of a function whose domain equals (1, 1) and whose range equals the range of f.
    d. Sketch the graph of a function whose domain equals the domain of f and whose range equals {1, 1}.
    There are two things you need to take into account to find the domain.

    First: Everything inside the square root is nonnegative.

    Second: The denominator can not be 0.
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  3. #3
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    So would the domain be:

    (-oo,-1)U[1, +oo)??
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  4. #4
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    i)For the domain of f take x+1 no to be 0 and the whole fraction (x-1)/(x+1) > or = to 0. Domain of f is (-infinite,-1) and [1,infinite)

    ii)if you substitute a with -a in the square root, then by changing the signs, the new fraction that you get is the inverse of the initial fraction so f(-a)=1/2. -f(a)=-2.
    1/f(a)=1/2. Be careful, if you substitute a with 1/a the fraction in the square root turns to be negative and f(1/a) does not exist!
    [(a-1)/(a+1)=4 if f(a)=2 and f(1/a)=square root of -(a-1)/(a+1)=-4 and so it does not exist]

    iii)the range of f is [0,infinite) as f is a square root
    A function with domain (-1,1) and range equals to the range of f is :
    1/[(1-x)*(x+1)]

    iv)Do you have to find a specific function and then sketch its graph? Or just sketch a line with the given domain and range for the x-axis and y-axis respectively?

    P.S. Sorry for not using an appropriate programme to write down the mathematical symbols, but i'm new to this forum. How did you wrote down the square root?
    Sorry for my English too, if i made any grammatic or syntax errors.
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  5. #5
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    It's called "LaTex" and the tutorial can be found here:

    http://www.mathhelpforum.com/math-help/latex-help/
    Last edited by goliath; January 9th 2010 at 07:50 PM.
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  6. #6
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    Thanks, and yes, I believe that it's just a graph with the respective domain and range.
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  7. #7
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    Then you can draw any line between -1 and 1 on the y-axis(for range) that it starts from -infinity and stops at -1 (open, -1 not included) and starts again from 1(closed, 1 included) to infinity on the x-axis. For example if you have a programme for graphs sketch sqrt((x^2-1)/x^2)).
    How old are you? Is this a problem for your school?
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  8. #8
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    I can't figure out the graph, could someone create a picture for me please?
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  9. #9
    Super Member bigwave's Avatar
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    here is the graph

    here is the graph of

    \sqrt{\frac{x^2-1}{x^2}}

    http://www.wolframalpha.com/input/?i=sqrt((x^2-1)%2F(x^2))
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  10. #10
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    Thanks bigwave!
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