The easiest way to add utility functions is to leave them at the global level:
function myUtilityFunction(x) { return "do something with "+x; }
Then, the simplest way to add a utility function (to a controller) is to assign it to $scope, like this:
$scope.doSomething = myUtilityFunction;
Then you can call it like this:
{{ doSomething(x) }}
or like this:
ng-click="doSomething(x)"
EDIT:
The original question is if the best way to add a utility function is through a service. I say no, if the function is simple enough (like the isNotString() example provided by the OP).
The benefit of writing a service is to replace it with another (via injection) for the purpose of testing. Taken to an extreme, do you need to inject every single utility function into your controller?
The documentation says to simply define behavior in the controller (like $scope.double): http://docs.angularjs.org/guide/controller