[Math] If $f(x)=3 f(1-x)+1$ for all $x$, the value of $f(2016)$

Question

If $$f(x)=3 f(1-x)+1$$
for all $x$, what is the value of $f(2016)$?

I am not sure how to do this, because I see two "$f$"s.

All I could try is substituting,

$$f(x)=3(1-2016)+1\\
=-6044$$

Which I am pretty sure wrong.

How do I deal with this question? when there is $f$ around a braket?

Thank you

Answer 1

Hint: $f(2016) = 3f(-2015) + 1$. But $f(-2015)= 3f(2016)+1$. Conclude