anonymous
  • anonymous
Find f^2(x), f^3(x), and f^n(x): F(x)=x-3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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lalaly
  • lalaly
\[f^2(x)=(x-3)^2\]
lalaly
  • lalaly
and the rest are the same
anonymous
  • anonymous
I'm not sure about that: for the example problem: F(x)=x+1 F^2(x)=x+2

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anonymous
  • anonymous
I'm studying iterated functions, if that helps at all
myininaya
  • myininaya
why is one f and the other F?
anonymous
  • anonymous
no difference- sorry
myininaya
  • myininaya
so you have f^2 not f^(2) so f^2 means to square f
myininaya
  • myininaya
like lala did
anonymous
  • anonymous
ah, i didnt realize it was different. It is \[f ^{2}(x)\]
anonymous
  • anonymous
Which is what I put in the problem... lol
lalaly
  • lalaly
what is the answer?
myininaya
  • myininaya
\[f^n(x)=(x-3)^n\]
anonymous
  • anonymous
Ok- but then the example makes no sense according to that
lalaly
  • lalaly
what are u studying about?
anonymous
  • anonymous
\[f ^{2}(x) =f(fx))\] =\[f(x)+1\] =x+3 Studying iterated functions
anonymous
  • anonymous
that example above is for f(x) = x+1
lalaly
  • lalaly
oh ok so it would be\[f(x-3)=(x-3)-3\]
anonymous
  • anonymous
ah, weird...I guess it makes sense, but I dont know why
anonymous
  • anonymous
i guess i just keep replacing x with x-3?
lalaly
  • lalaly
f(f(x)=f(x-3) replace the x with x-3
lalaly
  • lalaly
yeah exactly
anonymous
  • anonymous
yep- then how would i express that with n?
anonymous
  • anonymous
\[f ^{n}(x)=\]
myininaya
  • myininaya
so you are doing composition functions?
myininaya
  • myininaya
\[f^3(x)=f \circ f \circ f (x)\] is this what is meant by your notation?
anonymous
  • anonymous
no, or at least we haven't talked about it at all
anonymous
  • anonymous
it might be what is meant myinanaya
anonymous
  • anonymous
I'm just putting in what is in the book
myininaya
  • myininaya
so no where in the book does it say how f^3 is defined?
myininaya
  • myininaya
or f^n or whatever
lalaly
  • lalaly
http://en.wikipedia.org/wiki/Function_composition
lalaly
  • lalaly
like u said myin
anonymous
  • anonymous
for f(x) = x+1 \[f ^{3}(x)=f(f ^{2}(x))\] \[=f ^{2}(x)+1\] \[=(x+2)+1\] \[=x+3\]
myininaya
  • myininaya
lol lets assume what i thought is true okay?
lalaly
  • lalaly
u dont have to assume lol it is true
anonymous
  • anonymous
Sorry- I wasn't saying you were wrong earlier- I was saying I wasn't really studying this
lalaly
  • lalaly
it's okay i was wrong xD
myininaya
  • 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
  • myininaya
well i'm saying lalay f^2 can be read as f * f or f composed with f
myininaya
  • myininaya
there might be other notations for all i know
anonymous
  • anonymous
ah wow thank you so much! It makes a lot of sense now- sorry the notation was confusing
lalaly
  • lalaly
yeah :) well found about something new:D

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