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For a function f defined for nonzero x, suppose f(x) + 2f(1/x) = 3x and f(1/x) + 2f(x) = 3/x. Then the set of all possible values of f(x)

1. has exactly two members.
2. has more than two members.
3. is empty.
4. has exactly one member.

Correct answer: has exactly two members.

Solution

The equations provided create a system that can be solved for f(x) and f(1/x), leading to two distinct solutions for f(x) based on the symmetry and structure of the equations. This indicates that there are exactly two possible values for f(x) that satisfy both conditions.

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