08/18/2007, 12:19 AM

bo198214 Wrote:No, the slog function is only defined for bases greater than 1. For bases between 0 and 1, the tetration function is not one-to-one, so its inverse is not a function, because there are multiple values. It's much like saying that y=x^2 does not have an inverse function. y=sqrt(x) only covers part of the domain of the original function.andydude Wrote:If by my solution you mean through parabolic iteration ofNo, I meant the piecewise infinite differentiable definition of slog.

Isnt it defined for arbirtrary bases? (I think you wrote for base greater 1.)

Also, there's a question about whether you consider the slog function to only apply to the inverse of the function of iterated exponentials/logarithms from 1. For b=2, for example, the domain of slog is negative infinity to 2. However, you can perform iterated exponentials/logarithms from any real number as a starting point, so you could also include the graph for x>4 and the corridor between 2 and 4.

~ Jay Daniel Fox