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Math Help - domain/range help

  1. #1
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    domain/range help

    Hey guys, I'm having a problem with finding the domain and range of this function:

    f(x) = sqrt(X^2 - 1)

    this is what i thought:
    x|xER
    y|yER, y≥1

    but when you substitute 1 for x, you get y = 0, so it disproves what I thought to be correct.

    the second one I need help with is the function:

    f(x) = sqrt(x^2 - 1)/x-1

    i have no idea what the domain/range for that function could be, i've never seen something like that.
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  2. #2
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    f(x) = \sqrt{x^2 - 1}

    In order for the square root to be defined, x^2 - 1 must be a nonnegative number. Therefore, the domain is all x such that x^2 - 1 \geq 0 (can you put this in terms of intervals?). The range is y \geq 0 (why?).
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  3. #3
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    Smile

    hi
    the range is [0,\infty).
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  4. #4
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    wow thanks for the fast response.

    can
    <br />
x^2 - 1 \geq 0<br />

    be rephrased as

    x ≥ sqrt(1) ?

    thanks again
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  5. #5
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    Quote Originally Posted by snypeshow View Post
    wow thanks for the fast response.

    can
    <br />
x^2 - 1 \geq 0<br />

    be rephrased as

    x ≥ sqrt(1) ?

    thanks again
    Not exactly. You have x^2 \geq 1, which leads to the inequality |x| \geq 1. In summary: x can be negative.
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  6. #6
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    so would it be best to leave it as
    x^2 - 1 \geq 0?

    i also need help with:

    f(x) = sqrt(x^2 - 1)/x-1

    for domain and range
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  7. #7
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    Quote Originally Posted by snypeshow View Post
    so would it be best to leave it as
    x^2 - 1 \geq 0?
    The best way to write it would be x \leq -1 or x \geq 1.
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