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Math Help - Inequality question and don't know how this graph looks like?

  1. #1
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    Inequality question and don't know how this graph looks like?

    1) What is the x values for:
    x ( x - 5 ) > 0
    --> my answers are x>0 and x>5. And the book says, x<0 and x>5



    2) How does the graph of (4-x^2)^1/2 look like?


    Thanks in advance!
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  2. #2
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    Quote Originally Posted by dkssudgktpdy View Post
    1) What is the x values for:
    x ( x - 5 ) > 0
    --> my answers are x>0 and x>5. And the book says, x<0 and x>5



    2) How does the graph of (4-x^2)^1/2 look like?


    Thanks in advance!

    For (1), there are 2 cases to consider.

    when x>0 and x-5>0, this implies x>0 and x>5

    When x<0 and x-5<0 , this implies x<0 and x<5

    Take the intersection of the solutions.

    (2) Draw the graph y_1= 4-x^2 first.

    We see that this graph intersects the x-axis at -2 and 2, the y-axis at 4

    Now, for y_2=\sqrt{4-x^2}, for -2\leq x\leq 2 (Why? Think about the domain of a radical function)

    Previously, y_1 intersects the y-axis at 4, now y_2 intersects at 2.

    Put all these details together.
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  3. #3
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    so... for (1).. is the book answer wrong?
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  4. #4
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    Quote Originally Posted by dkssudgktpdy View Post
    so... for (1).. is the book answer wrong?
    No the book's answer is correct.
    Try some values: x=3,~x=6,~x=-2
    Which work and which do not work?
    Look at your answer.
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