Iterated functionsThe iteration operator * used in the lg* function can be applied to any...

Iterated functions

The iteration operator * used in the lg* function can be applied to any monotonically increasing function f(n) over the reals. For a given constant c ∈ R, we define the iterated function by

which need not be well-defined in all cases. In other words, the quantity is the number of iterated applications of the function f required to reduce its argument down to c or less.

For each of the following functions f(n) and constants c, give as tight a bound as possible on