Easy functional equation

Algebra Level 2

A function $f$ satisfies $f(x)+f(3x)=x^2+1$ for all real numbers $x$ .

If $f(2)+f(18)=6$ , determine the value of $f(6)$ .

2 solutions

Khang Nguyen Thanh
Aug 28, 2015

For $x=2$ , $f(2)+f(6)=5\qquad(1)$ .

For $x=6$ , $f(6)+f(18)=37\qquad(2)$ .

From $(1)$ and $(2)$ , we have $f(2)+f(18)+2f(6)=42$ or $2f(6)+6=42$ .

So, $f(6)=\boxed{18}$ .

Bill Bell
Oct 8, 2015

Same method as for the first answerer, using Sage.