How to solve an equation of functions...?

Question

so I have this equation: $f(x)+2f(5-x)=x$, and I need to find $f(1)$.

I tried to substitute $f(x)$ as y and $f(5-x)$ as $m$. There is only one equation, so I can't substitute when I get this:

$y+2m=x$

Can I somehow solve differently?

Answer 1

Hint: Put $x=1$ and $x=4$ in $$f(x)+2f(5-x)=x.$$

Answer 2

We can solve it as the following:

First put $x = 1$, we have $$f(1)+2f(4) = 1$$ where $f(4)$ and $f(1)$ are unknowns so we can't solve it yet.

Then put $x = 4$ in order to get a second equation with the same unknowns, we have $$f(4)+2f(1) = 4$$

Then, from the second equation, we have $f(4) = 4-2f(1)$. Putting it in the first equation yields $$f(1)+2(4-2f(1)) = 1 \implies -3f(1)+8=1 \implies f(1) = \frac{7}{3}$$