If 5 f x + 4 f 1 x = x 2 − 2 , ∀ x ≠ 0 and y = 9 x 2 f x , then y is strictly increasing in:

Step-by-step solution

Given: 5 f x + 4 f 1 x = x 2 - 2 . . . i Replacing x by 1 x . ⇒ 5 f 1 x + 4 f x = 1 x 2 - 2 . . . i i Using, i × 5 - i i × 4 ⇒ 25 f x + 20 f 1 x - 16 f x - 20 f 1 x = 5 x 2 - 10 - 4 x 2 + 8 ⇒ 9 f x = 5 x 2 - 4 x 2 - 2 Now, y = 9 f x × x 2 ⇒ y = 5 x 2 - 2 - 4 x 2 × x 2 ⇒ y = 5 x 4 - 2 x 2 - 4 ⇒ y ' = 20 x 3 - 4 x ⇒ y ' = 4 x 5 x 2 - 1 For function to be increasing y ' > 0 ⇒ x ∈ - 1 5 , 0 ∪ 1 5 , ∞