Domain of a Function with Sign Graph

[math4life]

Homework Statement

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

Homework Equations

f(x)= (3)/[(x²-4x)^1/2]

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.

 

[rock.freak667]

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.

 

[mg0stisha]

Sine graph?

 

[math4life]

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.

 

[Elucidus]

I suspect "sign graph" was the correct original intent.

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

$$\left\{ \begin{array}{r}{ x > 0 \\ x-4<0} \end{array}$$

$$\left\{ \begin{array}{rl} {x<0 \\ x-4 >0} \end{array}$$

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

+ + + + + + + + + + + - - - - - - + + + + + + + + +
___________________0________4________________

And from this one can determine the domain...

Solving $(x-2)^2 > 4 \Rightarrow |x-2| > 2$ is also valid.

--Elucidus

EDIT: Fixed a TeX gaffe.