A certain function f satisfies the equation f(x)+2*f(6-x) = x for all real numbers x. The value of f(1) is
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Given,
f(x) + 2 * f(6 - x) = x
Put x =1 => f(1)+2*f(6-1) = 1 => f(1) + 2*f(5) = 1 ---------- (1)
Put x = 5 => f(5)+2*f(6-5) = 5 => f(5) + 2*f(1) = 5
Put f(5) = 5 - 2*f(1) in the first equation (1)
=> f(1) + 2*(5 - 2*f(1)) = 1
=> f(1) + 10 - 4f(1) = 1
=> f(1) = 3