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Math Help - Nonlinear inequality

  1. #1
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    Nonlinear inequality

    Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set.


    I am stuck on where the line should start, I know it is a positive infinity, it appears as if it starts at -1, but its not correct.
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  2. #2
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    Start by reasoning on the Domain and Range.

    Domain doesn't help much.

    Range?

    x^{4} \ge 0

    x^{9} has the same sign as x.

    This restricts your solutions to x > 0.

    After that:

    x^{9} - x^{4} > 0

    x^{4} \cdot (x^{5} - 1) > 0

    Only x \ne 0 for x^{4}. How about the other piece?

    x^{5} - 1 = (x-1)(x^{4}+x^{3}+x^{2}+x+1)

    That big piece restricts nothing, being always greater than zero (0).

    The only piece of any remaining significance is (x - 1).

    This is a great problem to see if you were paying attention in class. Were you?
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  3. #3
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    Edit: sorry, didnt see tkhunny's post. Feel free to ignore this
    x^9>x^4
    if x \not = 0
    \frac{x^9}{x^4} >1
    x^5>1
    (x^5)^{1/5} >1^{1/5}
    x>1

    if x = 0 then 0^9\not > 0^4

    I know it is a positive infinity,
    Right
    Last edited by badgerigar; February 1st 2009 at 07:14 PM. Reason: TKhunny beat me to it
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  4. #4
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    Well it's like having x^3>1 then the cubic root "does the work," since this is just x>1. But this is actually the answer, but it does require a little bit of justification.
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