You can implement a search functionality using GetX in Flutter and display the search results on another page. Here's an example to guide you through this process:

Let's start by creating a simple app structure with two screens: the search screen and the result screen.

Search Screen:

This screen contains a text field for inputting the search query and a button to trigger the search.

Result Screen:

This screen displays the search results fetched from the API.

import 'package:flutter/material.dart';
import 'package:get/get.dart';

void main() {
  runApp(MyApp());
}

class DataController extends GetxController {
  var searchResults = [].obs;

  void fetchSearchResults(String query) async {
    // Perform API request here (replace with your actual API request logic)
    // For demonstration purposes, it's left empty.
    // Once you have actual API data, update the searchResults.
    // Example: final response = await http.get('your_api_url');
    // Then parse and assign data to searchResults.
    searchResults.value = [];
  }
}

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return GetMaterialApp(
      initialRoute: '/',
      getPages: [
        GetPage(name: '/', page: () => SearchScreen()),
        GetPage(name: '/result', page: () => ResultScreen()),
      ],
    );
  }
}

class SearchScreen extends StatelessWidget {
  final DataController dataController = Get.put(DataController());

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text('Search Screen'),
      ),
      body: Padding(
        padding: EdgeInsets.all(16.0),
        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: [
            TextField(
              onChanged: (value) {
                // Update the query in the controller
                dataController.fetchSearchResults(value);
              },
              decoration: InputDecoration(
                labelText: 'Search',
                border: OutlineInputBorder(),
              ),
            ),
            SizedBox(height: 20),
            ElevatedButton(
              onPressed: () {
                // Navigate to the result screen
                Get.toNamed('/result');
              },
              child: Text('Search'),
            ),
          ],
        ),
      ),
    );
  }
}

class ResultScreen extends StatelessWidget {
  final DataController dataController = Get.put(DataController());

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text('Result Screen'),
      ),
      body: Obx(() {
        final searchResults = dataController.searchResults;
        return ListView.builder(
          itemCount: searchResults.length,
          itemBuilder: (context, index) {
            final result = searchResults[index];
            return ListTile(
              title: Text(result['title']), // Replace with your actual data structure
              // Add onTap logic for each search result
              onTap: () {
                // Handle tap on search result
                print('Tapped on: ${result['title']}');
              },
            );
          },
        );
      }),
    );
  }
}