Find f^2(x), f^3(x), and f^n(x):
F(x)=x-3

Question

lalaly · Answer

$$f^2(x)=(x-3)^2$$

lalaly · Answer

and the rest are the same

anonymous · Answer

I'm not sure about that:

for the example problem:
F(x)=x+1
F^2(x)=x+2

anonymous · Answer

I'm studying iterated functions, if that helps at all

myininaya · Answer

why is one f and the other F?

anonymous · Answer

no difference- sorry

myininaya · Answer

so you have f^2 not f^(2)
so f^2 means to square f

myininaya · Answer

like lala did

anonymous · Answer

ah, i didnt realize it was different.  It is $$f ^{2}(x)$$

anonymous · Answer

Which is what I put in the problem... lol

lalaly · Answer

what is the answer?

myininaya · Answer

$$f^n(x)=(x-3)^n$$

anonymous · Answer

Ok- but then the example makes no sense according to that

lalaly · Answer

what are u studying about?

anonymous · Answer

$$f ^{2}(x) =f(fx))$$
=$$f(x)+1$$
=x+3

Studying iterated functions

anonymous · Answer

that example above is for f(x) = x+1

lalaly · Answer

oh ok so it would be$$f(x-3)=(x-3)-3$$

anonymous · Answer

ah, weird...I guess it makes sense, but I dont know why

anonymous · Answer

i guess i just keep replacing x with x-3?

lalaly · Answer

f(f(x)=f(x-3) replace the x with x-3

lalaly · Answer

yeah exactly

anonymous · Answer

yep- then how would i express that with n?

anonymous · Answer

$$f ^{n}(x)=$$

myininaya · Answer

so you are doing composition functions?

myininaya · Answer

$$f^3(x)=f \circ f \circ f (x)$$
is this what is meant by your notation?

anonymous · Answer

no, or at least we haven't talked about it at all

anonymous · Answer

it might be what is meant myinanaya

anonymous · Answer

I'm just putting in what is in the book

myininaya · Answer

so no where in the book does it say how f^3 is defined?

myininaya · Answer

or f^n or whatever

lalaly · Answer

http://en.wikipedia.org/wiki/Function_composition

lalaly · Answer

like u said myin

anonymous · Answer

for f(x) = x+1 
$$f ^{3}(x)=f(f ^{2}(x))$$
$$=f ^{2}(x)+1$$
$$=(x+2)+1$$
$$=x+3$$

myininaya · Answer

lol lets assume what i thought is true okay?

lalaly · Answer

u dont have to assume lol it is true

anonymous · Answer

Sorry- I wasn't saying you were wrong earlier- I was saying I wasn't really studying this

lalaly · Answer

it's okay i was wrong xD

myininaya · Answer

$$f(x)=x-3$$
$$f^2=f \circ f(x)=f(x-3)=(x-3)-3=x-6$$
$$f^3=f \circ f \circ f(x)=f(x-6)=(x-6)-3=x-9$$
$$f^4=f \circ f \circ f \circ f(x)=f(x-9)=(x-9)-3=x-12$$
so what is the pattern
f=x-3
f^2=x-3(2)
f^3=x-3(3)
f^4=x-3(4)
....
f^n=x-3(n)=x-3n

myininaya · Answer

well i'm saying lalay 
f^2 can be read as f * f
or f composed with f

myininaya · Answer

there might be other notations for all i know

anonymous · Answer

ah wow thank you so much! It makes a lot of sense now- sorry the notation was confusing

lalaly · Answer

yeah :) well found about something new:D