Question

For a real number x let [x] denote the largest number less than or equal to x. For x ∈ R let f (x) = [x] sin πx. Then

(A) f is differentiable on R.

(B) f is symmetric about the line x = 0.

 (C)  ∫ f(x) ∈[3,-3]  dx = 0

(D) For each real α, the equation f (x) – α = 0 has infinitely many roots

Answer 1

Correct option  (D) For each real α, the equation f (x) – α = 0 has infinitely many roots. 

Explanation:

f (x) = [x] sin πx

Not diff for ∀ x ∈ R.

Not sym about x = 0. 

f (x) = α will have ∞ solⁿ