1. ## domain

find the domain

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

2. Originally Posted by oneway1225
find the domain

f(x)=sqrt{x^2/x^2-6x+8}
You require the solutions to $\displaystyle \frac{x^2}{x^2 - 6x + 8} \geq 0$.

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

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

3. or easily, since what you want is

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

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.. )

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

5. Originally Posted by Krizalid
You don't have to consider $\displaystyle x^2,$ since it's always positive, just analize the denominator.
yeah, thank mistake.. it should be positive.. thus the product below should be positive..