Considering only the principal values of the inverse trigonometric functions, the domain of the function f x = cos - 1 x 2 - 4 x + 2 x 2 + 3 is

Step-by-step solution

Given, f x = cos - 1 x 2 - 4 x + 2 x 2 + 3 We know that domain of cos - 1   is  - 1 , 1 So, x 2 + 4 x + 2 x 2 + 3 ≤ 1 ⇒ x 2 - 4 x + 2 2 ≤ x 2 + 3 2 ⇒ x 2 - 4 x + 2 2 - x 2 + 3 2 ≤ 0 ⇒ 2 x 2 - 4 x + 5 - 4 x - 1 ≤ 0 Since 2 x 2 - 4 x + 5 > 0 as its discriminant D < 0 So, - 4 x - 1 ≤ 0 ⇒ x ≥ - 1 4 ⇒ x ∈ [ - 1 4 , ∞ )