Fix handling router prefix

fastapi/routing.py

@@ -1003,7 +1003,7 @@ class APIRouter(routing.Router):
             raise FastAPIError(
                 "APIRouter does not support mounting ASGI applications other than StaticFiles."
             )
-        self._mount(path=path, app=app, name=name)
+        self._mount(path=self.prefix + path, app=app, name=name)
 
     def _mount(self, path: str, app: ASGIApp, name: str | None = None) -> None:
         super().mount(path=path, app=app, name=name)

tests/test_apirouter_mount.py

@@ -8,18 +8,33 @@ from fastapi.testclient import TestClient
 
 
 @pytest.mark.parametrize("root_path", ["", "/v1"])
-def test_mount_static_files_to_apirouter(tmp_path: Path, root_path: str):
+@pytest.mark.parametrize(
+    ("router_prefix", "include_prefix", "request_prefix"),
+    [
+        ("", "", ""),
+        ("/router", "", "/router"),
+        ("", "/router_1", "/router_1"),
+        ("/router", "/router_1", "/router_1/router"),
+    ],
+)
+def test_mount_static_files_to_apirouter(
+    tmp_path: Path,
+    root_path: str,
+    router_prefix: str,
+    include_prefix: str,
+    request_prefix: str,
+):
     static_asset = tmp_path / "index.html"
     static_asset.write_text("Hello, World!")
 
-    router = APIRouter()
+    router = APIRouter(prefix=router_prefix)
     router.mount("/static", StaticFiles(directory=tmp_path), name="static")
 
     app = FastAPI(root_path=root_path or None)
-    app.include_router(router)
+    app.include_router(router, prefix=include_prefix)
 
     client = TestClient(app)
-    response = client.get(f"{root_path}/static/index.html")
+    response = client.get(f"{root_path}{request_prefix}/static/index.html")
     assert response.status_code == 200
     assert response.text == "Hello, World!"