hi everybody,
I've been looking at this problem for a while.
Given that f(x)+2f(8-x)=4 for all real x values find f(2).
Maybe I am missing something obvious.
Can anyone help?
Thanks in advance.
hi everybody,
I've been looking at this problem for a while.
Given that f(x)+2f(8-x)=4 for all real x values find f(2).
Maybe I am missing something obvious.
Can anyone help?
Thanks in advance.
$\displaystyle f(2)+2 f(6)=4 \Rightarrow$
$\displaystyle f(6)+2 f(2)=4 \Rightarrow$
$\displaystyle 3f(2)+3f(6)=8 \Rightarrow$
$\displaystyle f(2)+f(6)=\frac{8}{3}$
from the first equation
$\displaystyle f(2)=4-2f(6)$
plugging in
$\displaystyle 4-2f(6)+f(6)=\frac{8}{3} \Rightarrow$
$\displaystyle 4-f(6)=\frac{8}{3} \Rightarrow$
$\displaystyle f(6)=4-\frac{8}{3}=\frac{4}{3}$
$\displaystyle f(2)=4-2\cdot\frac{4}{3}=\frac{4}{3}$