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

Question

anonymous · Answer

I believe it is the second one.

anonymous · Answer

Thank you!

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

f is either -2 or 2.

anonymous · Answer

That is what I thougt. Chaos Theory project.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

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