Inception is the smallest phase in the project, and ideally it should be quite short. If the Inception Phase is long then it may be an indication of excessive up-front specification, which is contrary to the spirit of the Unified Process.
The following are typical goals for the Inception phase.
Establish a justification or business case for the project
Establish the project scope and boundary conditions
Outline the use cases and key requirements that will drive the design tradeoffs
Outline one or more candidate architectures
Identify risks
Prepare a preliminary project schedule and cost estimate
The Lifecycle Objective Milestone marks the end of the Inception phase.
Develop an approximate vision of the system, make the business case, define the scope, and produce rough estimate for cost and schedule.