If the domain of the function f (x) = x2 – 6x + 7 is (– ∞, ∞)

1.	If the domain of the function f (x) = x2 – 6x + 7 is (– ∞, ∞) then find the range of the function?
Answer» Let f (x) = y = x² – 6x + 7 ⇒ x² – 6x + 7 – y = 0 ⇒ x = \(\frac{6\,\pm \sqrt{36-4(7-y)}}{2} = 3\,\pm \sqrt{8+4y}\) For real values of x, 8 + 4y ≥ 0 ⇒ y ≥ – 2 ∴ For f (x) = x² – 6x + 7, the range is [– 2, ∞)

If the domain of the function f (x) = x2 – 6x + 7 is (– ∞, ∞) then find the range of the function?

Answer»

Let f (x) = y = x² – 6x + 7

⇒ x² – 6x + 7 – y = 0

⇒ x = \(\frac{6\,\pm \sqrt{36-4(7-y)}}{2} = 3\,\pm \sqrt{8+4y}\)

For real values of x, 8 + 4y ≥ 0

⇒ y ≥ – 2

∴ For f (x) = x² – 6x + 7, the range is [– 2, ∞)