The range of y = x^2 + 2x + 1/x^2 + 8x + 1 is (x∈R)

Question

The range of \(y = \frac{x^2 + 2x + 1}{x^2 + 8x + 1}\) is (x∈R)

(1) \((-\infty, -\frac 23] \cup [2,\infty)\)

(2) \((-\infty, 0]\cup[\frac 25, \infty)\)

(3) \((-\infty, \infty)\)

(4) \((-\infty, \frac{-2}5] \cup [1, \infty)\)

Answer 1

Correct option is (2) \((-\infty, 0]\cup[\frac 25, \infty)\)