Final answer:
The phrase that identifies one of the fundamental purposes of government in the Preamble of the US Constitution is to 'establish justice'. This is one of several core purposes which also include forming a more perfect union and providing for the common defense.
Step-by-step explanation:
One of the fundamental purposes of government as described in the Preamble to the United States Constitution is to establish justice. The Preamble outlines several core goals which include forming a more perfect union, providing for the common defense, and securing the blessings of liberty for current and future generations. These objectives highlight the intention behind the establishment of the government, which is to serve its citizens and ensure their well-being, safety, and fundamental freedoms.