Answer:
f(777) = 390
Step-by-step 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
