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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

Consider the function f x = cos - 1 ⁡ 3 x + sin - 1 ⁡ 3 x - 1 , then (where, ⋅ represents the greatest integer part of x )

Options

  1. Athe domain of f x is x ∈ - ∞ , 0
  2. Bthe range of f x is singleton
  3. Cf x is an even function
  4. Df x is an odd function

Correct answer

B. the range of f x is singleton

Step-by-step solution

For f x to be defined 3 x = 0 ,   1 ∴ 3 x ∈ 0 ,   2 ⇒ x ∈ - ∞ , log 3 ⁡ 2 Range of f x = cos - 1 ⁡ 0 + sin - 1 ⁡ - 1 , cos - 1 ⁡ 1 + sin - 1 ⁡ 0 ≡ 0 ∴ f x = 0   ∀ x ∈ - ∞ , log 3 ⁡ 2 So, the domain is not symmetric about the origin ∴ f x is neither even nor odd

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