Routers provide packet switching, packet filtering, internetwork communication, and path selection.

Router functions are responsible for managing and directing network traffic in a computer network. They play a crucial role in connecting different networks together and ensuring that data packets are delivered efficiently and securely. The correct answer is option 'E', as all of the given options describe the functions performed by a router. Let's explore each function in detail:

1. Packet Switching:
- Routers use packet switching to forward data packets from one network to another.
- When a router receives a data packet, it examines the destination IP address and determines the best path to forward the packet towards its destination.
- This process involves breaking the data into smaller packets and sending them separately, allowing for more efficient and reliable transmission.

2. Packet Filtering:
- Routers can perform packet filtering to control the flow of network traffic based on predefined rules or policies.
- These rules can be configured to allow or block specific types of traffic based on criteria such as source/destination IP addresses, ports, protocols, or other packet attributes.
- Packet filtering helps enhance network security by preventing unauthorized access and mitigating potential threats.

3. Internetwork Communication:
- Routers connect different networks together, enabling communication between devices on separate networks.
- They maintain a routing table that contains information about the available paths to different networks.
- By exchanging routing information with other routers, they can determine the most efficient paths for delivering data between networks.

4. Path Selection:
- Routers use routing protocols and algorithms to determine the best path for forwarding data packets.
- They consider factors such as network congestion, link availability, and latency to select the optimal path.
- Path selection ensures that data packets reach their destination in the most efficient and reliable manner.

In summary, routers perform various functions such as packet switching, packet filtering, internetwork communication, and path selection. These functions are essential for the proper functioning of computer networks and ensuring efficient data transmission.