Thanks. The first problem given in the reply is clear. The second problem illustrates however some difficulties and I am not sure if the "assume" facility is the right choice for implicit functions. Consider a slightly modified problem:

>restart;
>assume(a >1);
>assume(b >1);

>eq := x = a-x^b;

>additionally(eq);
>about(a);
>about(x);

Typing "about x" clearly shows that Maple understands that (-x+a-x^b=0). But consider the example a=b=2. In this case, x has solutions (1, -2). Typing

>coulditbe(x > 0);                           

Maple says: FAIL. Maple is unable to determine the restrictions the implicit function imposes on x.

(1) Is there a way to modify the assumptions on the variables so that Maple understands what I am looking for?

(2) Is the assume facility a good choice for the problem at hand? Maybe there is a different routine?

Thanks!