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# The function f : \mathbb{R} \to \mathbb{R} satisfies $f(x) + 2f(1 - x) = 3x^2$for all x. Find f(4).

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The function $$f : \mathbb{R} \to \mathbb{R}$$ satisfies $$f(x) + 2f(1 - x) = 3x^2$$  for all $$x$$. Find $$f(4)$$.

Nov 22, 2019
edited by Guest  Nov 22, 2019

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Hints:

$$f(4)+2f( a )= 3x^2\\ find \;\;a\\ then\\ f(a)+2f(b)=3x^2\\ find\;\;b\\$$

Now you can solve for  f(4) using simultaneous equations.