Numerical answer
A function f satisfies f(x) + 3f(4−x) = 2x + 1 for all real x. Find f(2).
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Answer: 1.25
Substituting x = 2 makes 4−x = 2 as well, so the equation becomes f(2) + 3f(2) = 2(2)+1 = 5, i.e. 4f(2) = 5, giving f(2) = 5/4 = 1.25. The key insight is spotting the self-paired value x = 4−x = 2, which avoids needing a second equation.
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