for the function f1(x)= 2x-1

______

x+1

fn+1(x)= f1(fn(x)), n>=1

it can be shown that f35 = f5.

Find f28.

how can i get this?(Worried)

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- Aug 30th 2009, 09:17 AMnh149inductive reasoning
for the function f1(x)= 2x-1

______

x+1

fn+1(x)= f1(fn(x)), n>=1

it can be shown that f35 = f5.

Find f28.

how can i get this?(Worried)

- Aug 31st 2009, 05:53 AMHallsofIvy
- Aug 31st 2009, 09:13 AMnh149i've been thinking of..
f28=f4 since f35=f5

because 35=5(7) and 28=4(7)..

is it right? - Aug 31st 2009, 10:30 AMOpalg
If then . So the inverse function to is given by .

But if then the maps repeat with period 30. Therefore , where . I think that's the least painful way to calculate .

You can check this by using HallsofIvy's calculation for to see that . This turns out to be the same as . So in fact the s repeat with period 6.