If $ f $ is a function such that $ 2 f(x)+f(2-x)=x^{2} $ then find value of $ f(4) $.

Question

If $ f $ is a function such that $ 2 f(x)+f(2-x)=x^{2} $ then find value of $ f(4) $.,

MARKS App · Accepted Answer

Given, 2 f x + f 2 - x = x 2 . . . i Substitute x by 2 - x in equation i we get, 2 f 2 - x + f x = 2 - x 2 . . . i i Now, i × 2 - i i we get, 3 f x = 2 x 2 - 2 - x 2 ⇒ f x = 1 3 2 x 2 - 2 - x 2 Then, f 4 = 1 3 2 4 2 - 2 - 4 2 = 1 3 32 - 4 = 28 3 = 9 . 33

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