Question

A function f, defined on the set of positive integers, has f(1) = 2 and f(2) = 3. Also f(f(f(n))) = n + 2 if n is even and f(f(f(n))) = n + 4 if n is odd. What is f(777)?

pls answer, I'm really confused

Answer 1

f(777) = 390

Explanation:

f(1) = 2 . . . . given

f(2) = f(f(1)) = 3 . . . . given

f(3) = f(f(f(1))) = 1+4 = 5

f(5) = f(f(3)) = f(f(f(2))) = 2+2 = 4

f(4) = f(f(5)) = f(f(f(3))) = 3+4 = 7

f(7) = f(f(4)) = f(f(f(5))) = 5+4 = 9

Then the sequence of sequential function values is ...

2, 3, 5, 4, 7, 9, 6, 11, 13, ... (pattern repeats in groups of 3)

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Each odd number of the form 4n+1 is the function value f(4n-1) = 4n+1.

Similarly, the next function value is f(4n+1) = (4n+1+3)/2.

Since 777 is 4(194) +1, we have ...

f(777) = (777+3)/2

f(777) = 390