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If f(x) = cos(log x), then the value of f(x)f(y) - 1/2 [f(x/y) + f(xy)] is:

1. 0
2. 1
3. -1
4. none of these

Correct answer: 0

Solution

The expression simplifies to zero due to the properties of the cosine function and logarithms, specifically using the identity for cosine of sums and the fact that the cosine function is even, leading to cancellation in the terms.

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