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 $\displaystyle x^2 - 6x + 8 < 0$.
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.. )