does anyone know why when solving the composite function f of f, when f(x)=3x, the answer comes out to be 3(3x)=9x?

Question

anonymous · Answer

yes

saifoo.khan · Answer

Correct.

anonymous · Answer

We just do not understand the first 3.  Why is it there?

anonymous · Answer

Let f(x)=3x. 
You are searching for f(f(x)). You can replace f(x) by 3x (per definition).
So you have f(3x). You can then replace 3x by another variable (let's say u=3x).
You have f(u). You can also say that if f(x)=3x, f(u)=3u.
So you finally have 3u. You can replace the u by its value (3x) and you get:
3(3x) = 9x

anonymous · Answer

We just do not understand the first 3.  Why is it there?

anonymous · Answer

ok, so the 3 takes on the place of the f?

saifoo.khan · Answer

v hav to insert, 3x in the place of x.

so 

3x
  ^
  |

here

3 (3x)

anonymous · Answer

We just do not understand the first 3.  Why is it there?

anonymous · Answer

ok.  What we were having trouble with is understanding why the 3 does not have an x with it.