# Math Help - Function question

1. ## Function question

Consider the function f: N --> R defined by
f(0) = 2
f(n+1) = f(n) + n - 2

Compute f(1), f(2), f(3).

I know how to do this, but I was just wondering what is "n" - I mean f(n) for f(1) is 2, but is n just 1 for f(1) or 0?

2. Originally Posted by brumby_3
Consider the function f: N --> R defined by
f(0) = 2
f(n+1) = f(n) + n - 2

Compute f(1), f(2), f(3).

I know how to do this, but I was just wondering what is "n" - I mean f(n) for f(1) is 2, but is n just 1 for f(1) or 0?
$f(1)=f(0+1)=f(0)+0-2~\&~f(2)=f(1+1)=f(1)+1-2$

3. Originally Posted by Plato
$f(1)=f(0+1)=f(0)+0-2~\&~f(2)=f(1+1)=f(1)+1-2$
Thank you Plato!

4. For $f(n+1) = f(n) + n - 2$ make $n=0$ you get

$f(0+1) = f(0) + 0 - 2 \implies f(1) = 2 + 0 - 2 = 0$

Now make $n=1$

5. Thanks pickslides, I've got it