- #1

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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.