Question

f(x)+2f(1-x)=x^2 +2then f(x)=? is there 2 different ways to solve this ?

Answer 1

Given f(x) + 2f(1 - x) = x^2 + 2----------(1)

put x = (1 - x)

f(1 - x) + 2f(1 - (1 - x) = (1 - x)^2 + 2

f(1 - x) + 2f(x) = (1 - x)^2 + 2  multiply by 2

2f(1 - x) + 4f(x) = 2(1 - x)^2 + 4-------------(2)

subtracting eqn (1) and (2)

2f(1 - x) + 4f(x) = 2(1 - x)^2 + 4-

 2f(1 - x) + f(x) = x^2 + 2

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       3f(x) = 2(1 - 2x + x^2) + 4

   3f(x) = x^2 - 4x + 4

    f(x) = (x - 2)^2 / 3