domain

**oneway1225** · December 23rd 2008, 06:46 PM

find the domain

f(x)=sqrt{x^2/x^2-6x+8}

**mr fantastic** · December 23rd 2008, 06:51 PM

Originally Posted by oneway1225

find the domain

f(x)=sqrt{x^2/x^2-6x+8}

You require the solutions to $\frac{x^2}{x^2 - 6x + 8} \geq 0$ .

Case 1: Solve the simultaneous inequations $x^2 \geq 0$ AND $x^2 - 6x + 8 > 0$ .

Case 2: Solve the simultaneous inequations $x^2 \leq 0$ AND $x^2 - 6x + 8 < 0$ .

**kalagota** · December 23rd 2008, 08:58 PM

or easily, since what you want is

$\dfrac{x^2}{x^2-6x+8} = \dfrac{x^2}{(x-2)(x-4)} \geq 0$

you may want to create this table of signs..

just complete the table.. and determine which interval do you need.. (i hope this is familiar to you..

)

**Krizalid** · December 24th 2008, 06:58 AM

You don't have to consider $x^2,$ since it's always positive, just analize the denominator.

**kalagota** · December 24th 2008, 07:15 AM

Originally Posted by Krizalid

You don't have to consider $x^2,$ since it's always positive, just analize the denominator.

yeah, thank mistake.. it should be positive.. thus the product below should be positive..

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