SOLUTION: If {{{ f(x) = 1 + (1/x) }}}, find f(f(f(1))).

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Question 996381: If +f%28x%29+=+1+%2B+%281%2Fx%29+, find f(f(f(1))).


Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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If +f%28x%29+=+1+%2B+%281%2Fx%29+, find f(f(f(1))).
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f(1) = 1 + 1%2F1 = 1 + 1 = 2.

f(f(1)) =     ( substitute  2  as  f(1) )     = f(2) = 1 + 1%2F2 = 11%2F2 = 3%2F2.

f(f(f(1))) =     ( substitute  3%2F2  as  f(f(1)) )      = f(3%2F2) = 1 + 1%2F%28%283%2F2%29%29 = 1 + 2%2F3 = 12%2F3.