What are the additional transistors used for in this hex inverter?
This is a classic TTL gate.

To ensure that all TTL devices present the same load, the input is always a transistor with the emitter at the actual input (multi-input devices have multiple input emitters).

The next transistor is a drive stage and the output is a totem-pole stage which can both source (output high) and sink (output low) current.

The output current in the high and low states are different (and for a single fan out match the input current for TTL devices).