anonymous one year ago When you start with the function f^2(1)=2*2*1=4, if asked to repeat the process with an initial value of -1, does that mean :f^2(-1)=2*2*1 OR f^2(-1)=2*2*-1

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1. anonymous

I believe it is the second one.

2. anonymous

Thank you!

3. anonymous

i would love to know what $f^2(1)=2*2*1=4$ means

4. anonymous

It is reasonable to assume that because f(1) is there that the 1 in the equation is the x spot for f(x).

5. anonymous

f is either -2 or 2.

6. anonymous

That is what I thougt. Chaos Theory project.

7. anonymous

Probably 2. However, you can't really figure out how 2 is made because they don't give you the original function.

8. anonymous

f(x)=2x given initial value of 1

9. anonymous

iterations..f(1) = 2*1 = 2 , f^2(1) = 2*2*1 =4, f^3 (1) = 2*2*2*1=8. Replace initial value with -1 to find pattern.

10. anonymous

maybe it is $f(x)=2x\\ f(-1)=-2\\ f^2(-1)=2\times 2\times -1=-4\\ f^3(-1)=-8 ...\\ f^n(-1)=-2^n$