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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

Consider the function f x = c o s - 1 2 x + s i n - 1 2 x - 1 , then (where [.] represents the greatest integer part function)

Options

  1. ADomain of f x is x ∈ – ∞ , 0
  2. BRange of f x is singleton
  3. Cf x is an even function
  4. Df x is an odd function

Correct answer

B. Range of f x is singleton

Step-by-step solution

For f x to be defined 2 x = 0 , 1 ∴ 2 x ∈ 0,2 ⇒ x ∈ – ∞ , 1 Range c o s - 1 0 + s i n - 1 - 1 , c o s - 1 1 + s i n - 1 0 ≡ 0 ∴ f x = 0 ∀ x ∈ – ∞ , 1 So, Domain is not symmetric about the origin ∴ f x is neither even nor odd

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