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NTA Abhyas JEE Main2020MathematicsFunctionsPractice

For the function f x = s i n π x × c o s - 1 x , choose the correct option. (where . represents the greatest integer function)

Options

  1. ADomain of f x ∈ - 1,1
  2. BRange of f x contains exactly two elements
  3. Cf x is an identity function
  4. Df x is a constant function

Correct answer

D. f x is a constant function

Step-by-step solution

For any x ∈ R , we know, sin ⁡ π x = 0 ∴ f x = 0 ,   ∀ x ∈ - 1,2 ∵ - 1 ≤ x ≤ 1   f o r   c o s - 1 x   t o   be   d e f i n ed ∴ Domain x ∈ - 1,2 ⇒ Range = 0 ∴ f x is a constant function

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