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Let f(x)={x21 if x is a multiple of 3 and 7,3x if x is only a multiple of 7,7x if x is only a multiple of 3,x+3 if x is not a multiple of 3 or 7.

 

If fa(x) means the function is nested a times (for example, f2(x)=f(f(x))), what is the smallest value of a greater than 1 that satisfies f(2)=fa(2)?

 Aug 25, 2023
 #1
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We have that f(2)=221 f2(2)=f(f(2))=f(221) =3221=27 f3(2)=f(f2(2))=f(27) =727=2 f4(2)=f(f3(2))=f(2)=221.Since f4(2)=f(2), the smallest value of a greater than 1 that satisfies f(2)=fa(2) is 4​.

 Aug 25, 2023
 #2
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Aha tysm!

dolphinia  Aug 27, 2023

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