How to make a function return observable in Flutter using GetX?

I am trying to convert a code uses stateful widget and provider package to a code with using staless widget and GetX package, but I don't know what can I do for the following getter function?

  bool get isAuth {
    return token != null;
  }

This function checks out if the token exist or not, and the token itself comes from the following function:

  String? get token {
    if (_expiryDate != null &&
        _expiryDate!.isAfter(DateTime.now()) &&
        _token != null) {
      return _token;
    }
    return null;
  }

I don't know how to modify this part of code to make the isAuth variable observable, then I can use it inside the main.dart to direct the application either into the Auth screen or Home screen?

Edit: I tried the code suggested in the answer by @S. M. JAHANGIR but I don't know what should I do for the Obx part in main.dart file? The following is the main.dart file:

void main() {
  Get.put(MenuController());
  Get.put(NavigationController());
  Get.put(AuthController());
  Get.put(AuthCard);
  runApp(MyApp());
}

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return GetMaterialApp(
      initialRoute: Obx(()=>AuthController.instance.isAuth
          ? homeScreenRoute
          : authenticationScreenRoute),

      unknownRoute: GetPage(
          name: '/not-found',
          page: () => PageNotFound(),
          transition: Transition.fadeIn),
      getPages: [
        GetPage(
            name: rootRoute,
            page: () {
              return SiteLayout();
            }),
        GetPage(
            name: authenticationScreenRoute,
            page: () => const AuthenticationScreen()),
        GetPage(name: homeScreenRoute, page: () => HomeScreen()),
      ],
      debugShowCheckedModeBanner: false,
      title: 'BasicCode',
      theme: ThemeData(
        scaffoldBackgroundColor: light,
        textTheme: GoogleFonts.mulishTextTheme(Theme.of(context).textTheme)
            .apply(bodyColor: Colors.black),
        pageTransitionsTheme: const PageTransitionsTheme(builders: {
          TargetPlatform.iOS: FadeUpwardsPageTransitionsBuilder(),
          TargetPlatform.android: FadeUpwardsPageTransitionsBuilder(),
        }),
        primarySwatch: Colors.blue,
      ),
      // home: AuthenticationPage(),
    );
  }
}

And I get the following error message for this line of the code initialRoute: Obx(()=>AuthController.instance.isAuth? homeScreenRoute: authenticationScreenRoute):

The argument type 'Obx' can't be assigned to the parameter type 'String?'.

I also tried initialRoute: Obx(()=> AuthController.instance.isAuth ? homeScreenRoute : authenticationScreenRoute) as String? But it gives me a new error:

The return type 'String' isn't a 'Widget', as required by the closure's context.

If you want to make the isAuth getter observable, you can simply do:

RxBool get isAuth {
   return RxBool(token != null);
 }

But a more convenient way to do this is:

final _isAuth = false.obs;

bool get isAuth {
 _isAuth.value= token != null;
 return _isAuth.value;
}

And use it like:

Obx(()=> isAuth? codeIfAuthenticated: codeIfNotAuthenticated)