Suppose f and g are functions having the same domains such that
 f is monotonic increasing/decreasing on a given interval iff g is
monotonic increasing/decreasing on that same interval.

Is there a name for such pairs of functions?

(I ask this question since it arises in stat estimation theory with
the MLE: very often one does not work with the likelihood function,
but rather the log of the likelihood function or in fact any quantity
proportional to the log likelihood function, given that the constant
of proportionality is positive. The idea here being that x is a max of
the pdf iff x is a max of the log of the pdf since the functions f=pdf
and g=log(pdf) have this relationship described above.)

Thanks,