Explanation:

State Function:
A state function is a property of a system that depends only on the current state of the system and not on the path taken to reach that state. In other words, a state function is independent of the process or path by which the system reached its current state.

Work as a State Function:
Work is not a state function. It is a process function. A process function is a function that depends on the path taken to reach a particular state. Work is the transfer of energy between a system and its surroundings. The amount of work done depends on the specific process or path taken to reach a particular state. Therefore, work is not solely determined by the initial and final states of the system, making it a process function rather than a state function.

Temperature as a State Function:
Temperature is a state function. It is a property of a system that depends only on its current state and is independent of the process or path taken to reach that state. The temperature of a system can be determined by measuring the average kinetic energy of its particles, which is a characteristic of the system's state.

Change in State:
The change in state of a system is completely defined when the initial and final states are specified. This means that if we know the initial state of a system and the final state it reaches, we can determine all the properties and characteristics of the system during the process of changing from the initial state to the final state.

Work at the Boundary of the System:
Work appears at the boundary of the system. When a system undergoes a process, it can exchange energy with its surroundings in the form of work. This work can be done on the system by the surroundings, or it can be done by the system on the surroundings. Work is a form of energy transfer and can appear as mechanical work (e.g., when a gas expands against a piston) or other forms of work (e.g., electrical work, gravitational work).

Therefore, the false statement is option A: Work is a state function. Work is not a state function but a process function.