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If f x = x 3 + x + 1 t a n π x (where, x represents the greatest integer part of x ), then

Options

  1. Adomain of f x is R - 2 n + 1 π 2 , n ∈ Ι
  2. Brange of f x ∈ R
  3. Cf x is an even function
  4. Df x is a non-periodic function

Correct answer

C. f x is an even function

Step-by-step solution

∀ x ∈ R ⇒ x is an integer ∴   π x = n π ,   n ∈ Ι and tan π x = t a n n π = 0 ∴ f x = 0 ∀ x ∈ R ∴ f x is an even function

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