Problem

Problem

Given the function

f(x)

such that

2f(x) + xf\left(\frac{1}{x}\right) - 2f\left(\sqrt{2} \sin \pi \left(x + \frac{1}{4}\right)\right) = 4 \cos^2 \frac{\pi x}{2} + x \cos \frac{\pi}{x},

then which one of the following is correct? (a)

f(2) + f(1/2) = 1

(b)

f(1) = -1

, but the values of

f(2)

,

f(1/2)

cannot be determined (c)

f(2) + f(1) = f(1/2)

(d)

f(2) + f(1) = 0

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