1. The problem statement, all variables and given/known data Find the image set of fucntion fx = (2x^2 + 2x + 1)/(x^2 + x - 1 ) The attempt at a solution 1. multiply the denominator with y and then assume x is real i get (y-2)^2 - 4(y - 2)(-y-1) => 0 5y^2 - 8y - 4 => 0 y = 2 and y = -2/5 But the answer is y => 2 and y =< 2/5 not -2/5 Then i substitute the -2/5 to the original equation and i got complex solution. So is it mean that -2/5 is out. And 2nd, why the answer is 2/5? And 3rd, how to test the validity of the range like whether it is a<y<b or y < a , y> a? I sketched using tools on http://graph.seriesmathstudy.com/ and -2/5 is valid asymptote.