x(x^2 – 2x + 1) < 0 x (x-1) (x-1) < 0 looks like x = 0 and x = 1 are values where things might change.... Case A: x < 0: (-) ( -) (-) < 0 ? TRUE or plug in a value less than zero: x=-2: (-2)(-3)(-3) = -18 < 0 TRUE Case B 0 < x <1: (+)(-)(-) <0? ... FALSE Case C: x > 1: (+) (+) (+) <0? ... FALSE At x = 0 or x = 1, equation gives ZERO < 0? FALSE ... only x<0 makes equation negative. 2. since you can only have real numbers in the radical sign, any value of x that makes the radicand (what's inside) negative will not work. values of x that give zero or positive in the radical sign are the DOMAIN. factor inside of G(x) = (x^2-6x+8)^(1/2). sqrt[ (x-2)(x-4)] things might change at x=2 and x = 4.... figure out what value of x make (x-2)(x-4) positive. that's the DOMAIN. g.l.