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Homework Help: Domain of a Function with Sign Graph

  1. Aug 26, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the domain of the function. You will need a sign graph. Answer in interval notation.

    2. Relevant equations

    f(x)= (3)/[(x2-4x)1/2]

    3. The attempt at a solution
    No clue - I don't know how to use a sign graph or what the positive/negative results mean as solutions on a number line.
  2. jcsd
  3. Aug 26, 2009 #2


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    Homework Helper

    I am not sure what a sign graph is.

    But the domain is the x values for f being defined. There is a square root, so what is inside can't be less than zero. Since it is a fraction, the denominator can't be zero.
  4. Aug 26, 2009 #3
    Sine graph?
  5. Aug 27, 2009 #4
    I meant sine graph instead of sign graph. So what do I do? Should I set the denominator to greater than or equal to zero and solve?

    I tried solving using the above method but I think my math is wrong. Nonetheless it is wrong because my teacher wants a sine graph on a number line...

    1) (sqrt(x2-4x) greater than or equal 0
    2) x2-4x greater than or equal 0 (this step is wrong I'm pretty sure - squaring both sides)
    3) x2-4x+4 greater than equal 4
    4) (x-2)2 greater than equal 4

    .... ? I still need the sine graph.
  6. Aug 27, 2009 #5
    I suspect "sign graph" was the correct original intent.

    When solving [itex]x^2-4x = x(x-4) > 0[/itex], this boils down to the cases:

    [tex]\left\{ \begin{array}{r}{ x > 0 \\ x-4<0} \end{array}[/tex]

    [tex]\left\{ \begin{array}{rl} {x<0 \\ x-4 >0} \end{array}[/tex]

    This can also be illustrated with a sign graph of x^2 - 4x:

    + + + + + + + + + + + - - - - - - + + + + + + + + +

    And from this one can determine the domain...

    Solving [itex](x-2)^2 > 4 \Rightarrow |x-2| > 2[/itex] is also valid.


    EDIT: Fixed a TeX gaffe.
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