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

Question

0

826

2

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

Guest Nov 22, 2019

edited by Guest Nov 22, 2019

Melody · Answer 1 · 2019-11-22T06:20:26

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.

Please no one provide a full answer.

The function f : \mathbb{R} \to \mathbb{R} satisfies f(x)+2f(1−x)=3x2f(x) + 2f(1 - x) = 3x^2for all x. Find f(4).