# Thread: Given that f(x)+2f(8-x)=4 for all real x values find f(2).

1. ## Given that f(x)+2f(8-x)=4 for all real x values find f(2).

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?

2. ## Re: Given that f(x)+2f(8-x)=4 for all real x values find f(2).

Originally Posted by Melody2
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?

$f(2)+2 f(6)=4 \Rightarrow$

$f(6)+2 f(2)=4 \Rightarrow$

$3f(2)+3f(6)=8 \Rightarrow$

$f(2)+f(6)=\frac{8}{3}$

from the first equation

$f(2)=4-2f(6)$

plugging in

$4-2f(6)+f(6)=\frac{8}{3} \Rightarrow$

$4-f(6)=\frac{8}{3} \Rightarrow$

$f(6)=4-\frac{8}{3}=\frac{4}{3}$

$f(2)=4-2\cdot\frac{4}{3}=\frac{4}{3}$

3. ## Re: Given that f(x)+2f(8-x)=4 for all real x values find f(2).

Originally Posted by romsek
$f(2)+2 f(6)=4 \Rightarrow$

$f(6)+2 f(2)=4 \Rightarrow$

$3f(2)+3f(6)=8 \Rightarrow$

$f(2)+f(6)=\frac{8}{3}$
I am sorry Romsek but this doesn't make any sense to me.

f(2) + 2f(6) = 4 Good, that's given
but
the next 2 lines are a mystery to me.

4. ## Re: Given that f(x)+2f(8-x)=4 for all real x values find f(2).

Originally Posted by Melody2
I am sorry Romsek but this doesn't make any sense to me.

f(2) + 2f(6) = 4 Good, that's given
but
the next 2 lines are a mystery to me.
the first line is your expression with x=2

the second line is the same w/x=6

the 3rd line is the sum of the 1st and 2nd lines

the 4th line simple divides both sides by 3.

5. ## Re: Given that f(x)+2f(8-x)=4 for all real x values find f(2).

Of course. Thanks Romsek. I really appreciate it.

6. ## Re: Given that f(x)+2f(8-x)=4 for all real x values find f(2).

clear?

Ah, I shouldn't have had a $\Rightarrow$ after the first line.

The first doesn't imply the second line.

Sorry.

7. ## Re: Given that f(x)+2f(8-x)=4 for all real x values find f(2).

All sorted. Thanks. The arrow did confuse me but also I didn't understand what w/x meant . I thought it was some kind of ratio. lol