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Algebra Difficulty 4.0 AIME Find the answer China

Suppose f(x)f(x) is an odd function with domain R\mathbb{R}. If f(1)=2f(1) = 2, f(2)=3f(2) = 3, then the value of f(f(1))f(f(-1)) is ______.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

By the given conditions we have f(1)=f(1)=2f(-1) = -f(1) = -2. Therefore,
f(f(1))=f(2)=f(2)=3. f(f(-1)) = f(-2) = -f(2) = -3.

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