Question: How to define an implicit function in Maple (II)?

I have problems with a variable that is given only implicitly. Maple provides incorrect answers but I am not sure where I make the mistake. Thanks for any comments! Here is what I do:

(1) I use "assume" to set properties of two paramters a and b.

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

(2) Since the variable "x" is given only implicitly, I define an implicit function following the description in the thread "How to define an implicit function in Maple?".

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

(3) Given that a and b are positive, x cannot be zero but I get the following output.

> is(x > 0);
                             false
> is(x < 0);
                             false
> is(x = 0);
                             false
> coulditbe(x > 0);
                              true
> coulditbe(x = 0);
                              true
> coulditbe(x < 0);
                              true

Does anyone know where I make a mistake? Does the command "eq := x = a+x^b" impose any restrictions on x given the assumptions on the parameters a and b? If not, is it possible to impose restrictions on a variable that is given only implicitly?

Thanks!