Question

If 2f(x) + xf(1/x) - 2f(|√sin π(x + 1/4)|) = 4cos²(πx/2) + x cos π/x, ∀x ∈ R-{0} then which of the following statements(s) is/are true?

(A)  f(2) + f(1/2) = 1

(B) f(2) + f(1) = 0

(C)  f(2) + f(1) = f(1/2)

(D)  f(1) + f(1/2) = 1

Answer 1

Correct option (A)(B)(C)

Explanation:

Replace x by 2, 2f(2) + 2f(1/2) - 2f(1) = 4