Find the domain of the following functions.fx = \(\sqrt{log(x^2-6x+6)

1.	Find the domain of the following functions.fx = \(\sqrt{log(x^2-6x+6)}\)fx = √log(x2 - 6x +6)
Answer» f(x) = \(\sqrt{x-x^2} + \sqrt {5-x}\) For f to be defined, log (x² – 6x + 6) ≥ 0 ∴ x² – 6x + 6 ≥ 1 ∴ x² – 6x + 5 ≥ 0 ∴ (x – 5)(x – 1) ≥ 0 ∴ x ≤ 1 or x ≥ 5 …..(i) [∵ The solution of (x – a) (x – b) ≥ 0 is x ≤ a or x ≥ b, for a < b] and x² – 6x + 6 > 0 ∴ (x – 3)² > -6 + 9 ∴ (x – 3)² > 3 ∴ x < 3 – √3 0r x > 3 + √3 ……..(ii) From (i) and (ii), we get x ≤ 1 or x ≥ 5 Solution set = (-∞, 1] ∪ [5, ∞) ∴ Domain of f = (-∞, 1] ∪ [5, ∞)

Find the domain of the following functions.fx = \(\sqrt{log(x^2-6x+6)}\)fx = √log(x2 - 6x +6)

Answer»

f(x) = \(\sqrt{x-x^2} + \sqrt {5-x}\)

For f to be defined,

log (x² – 6x + 6) ≥ 0

∴ x² – 6x + 6 ≥ 1

∴ x² – 6x + 5 ≥ 0

∴ (x – 5)(x – 1) ≥ 0

∴ x ≤ 1 or x ≥ 5 …..(i)

[∵ The solution of (x – a) (x – b) ≥ 0 is x ≤ a or

x ≥ b, for a < b]

and x² – 6x + 6 > 0

∴ (x – 3)² > -6 + 9

∴ (x – 3)² > 3

∴ x < 3 – √3 0r x > 3 + √3 ……..(ii)

From (i) and (ii), we get

x ≤ 1 or x ≥ 5

Solution set = (-∞, 1] ∪ [5, ∞)

∴ Domain of f = (-∞, 1] ∪ [5, ∞)