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

- anonymous

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

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- lalaly

\[f^2(x)=(x-3)^2\]

- lalaly

and the rest are the same

- anonymous

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

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## More answers

- anonymous

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

- myininaya

why is one f and the other F?

- anonymous

no difference- sorry

- myininaya

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

- myininaya

like lala did

- anonymous

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

- anonymous

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

- lalaly

what is the answer?

- myininaya

\[f^n(x)=(x-3)^n\]

- anonymous

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

- lalaly

what are u studying about?

- anonymous

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

- anonymous

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

- lalaly

oh ok so it would be\[f(x-3)=(x-3)-3\]

- anonymous

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

- anonymous

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

- lalaly

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

- lalaly

yeah exactly

- anonymous

yep- then how would i express that with n?

- anonymous

\[f ^{n}(x)=\]

- myininaya

so you are doing composition functions?

- myininaya

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

- anonymous

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

- anonymous

it might be what is meant myinanaya

- anonymous

I'm just putting in what is in the book

- myininaya

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

- myininaya

or f^n or whatever

- lalaly

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

- lalaly

like u said myin

- anonymous

for f(x) = x+1
\[f ^{3}(x)=f(f ^{2}(x))\]
\[=f ^{2}(x)+1\]
\[=(x+2)+1\]
\[=x+3\]

- myininaya

lol lets assume what i thought is true okay?

- lalaly

u dont have to assume lol it is true

- anonymous

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

- lalaly

it's okay i was wrong xD

- myininaya

\[f(x)=x-3\]
\[f^2=f \circ f(x)=f(x-3)=(x-3)-3=x-6\]
\[f^3=f \circ f \circ f(x)=f(x-6)=(x-6)-3=x-9\]
\[f^4=f \circ f \circ f \circ f(x)=f(x-9)=(x-9)-3=x-12\]
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

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

- myininaya

there might be other notations for all i know

- anonymous

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

- lalaly

yeah :) well found about something new:D

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