NTA Abhyas JEE Main2020MathematicsFunctionsPractice

The solution set of the inequality tan - 1 ⁡ x 2 ≤ tan - 1 ⁡ x + 6 is

Options

A- tan ⁡ 2 , tan ⁡ 3
Btan ⁡ 2 , - tan ⁡ 3
Ctan ⁡ 2 , tan ⁡ 3
D- ∞ , ∞

Correct answer

D. - ∞ , ∞

Step-by-step solution

Let tan − 1 x = u So, inequality becomes u 2 − u − 6 ≤ 0 ⇒ − 2 ≤ u ≤ 3 So, − 2 ≤ tan − 1 x ≤ 3 As − π 2 < tan − 1 x < π 2 ⇒ − 2 ≤ tan − 1 x ≤ 3 , ∀ x ∈ R Therefore, the solution set of the inequality tan - 1 ⁡ x 2 ≤ tan - 1 ⁡ x + 6 is - ∞ , ∞

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