$ f: \mathbb{N} \rightarrow \mathbb{N} $
$f(n) + f(f(n)) = 6n $
Find $ f(n)$
Instructive FE (I desperately need that topic list)
Re: Instructive FE (I desperately need that topic list)
Some hints.
First try to guess the answer. Done? Let's move on.
Now there aren't a lot of things you can do in this problem apart from proving $f$ is injective, and even that doesn't yield much. So you can only plug in values. Plug in $n=1$. First assume that $f(1)=1$. Keep reiterating the values to see what happens. Does it become negative at some point? If so, try with more values and see if something becomes negative.
Finally, try to prove this.
First try to guess the answer. Done? Let's move on.
Now there aren't a lot of things you can do in this problem apart from proving $f$ is injective, and even that doesn't yield much. So you can only plug in values. Plug in $n=1$. First assume that $f(1)=1$. Keep reiterating the values to see what happens. Does it become negative at some point? If so, try with more values and see if something becomes negative.
Finally, try to prove this.