CAT 2023 Slot 2 · Quant · Functions · hard

A function f satisfies f(x) + 2f(6−x) = 3x for all real x. Find f(2).

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Answer: 6

Replace x with (6−x): f(6−x) + 2f(x) = 3(6−x) = 18−3x. From the original equation, f(6−x) = (3x − f(x))/2. Substituting: 2f(x) + (3x−f(x))/2 = 18−3x → 4f(x) + 3x − f(x) = 36 − 6x → 3f(x) = 36 − 9x → f(x) = 12 − 3x. So f(2) = 12 − 6 = 6.

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