Trail and Error!

Algebra Level pending

For a function \(f(x)\),

\(f(1) - f(-1) = 6\\f(2) - f(-2) = 3\\f(3) - f(-3) = 2\\f(6) - f(-6) = 1\)

If the above information holds true, and \(f(x) - f(-x)\) follows same pattern for all values of \(x\), find the value of \(f(12) - f(-12)\)

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