Final answer:
The United States Air Force, which became its own branch after WWII, often conducts Air Expeditionary Task Force (AETF) operations, as seen in missions like the Berlin Airlift and roles within the International Security Assistance Force under NATO.
Step-by-step explanation:
The function or organization established to operate with an air expeditionary task force (AETF) is most closely associated with military and defense efforts involving air force operations. While the question does not specify a particular time period or conflict, it is notable that the United States Air Force (USAF), which became an independent service branch after World War II, has conducted various AETF operations.
For instance, during the Berlin Airlift, the USAF undertook a massive mission to supply the Western sector of Berlin via cargo planes. Another example of an AETF in operation can be seen in the role of the International Security Assistance Force (ISAF) under NATO leadership. The US, as a part of the international coalition, contributed troops to both the ISAF and Operation Enduring Freedom, with the objective of stabilizing and reconstructing Afghanistan, pursuing al-Qaeda, and ensuring security in the region.