fungi exist as single cells or as branching networks of multicellular filaments with a very large surface area. what is the function of the filaments?

Their large surface area aids in nutrient absorption.

Explanation:

The main parts of a fungi's body include long, branched hair-like projections called the filaments and an outer cell wall; chitin. The hair-like projections are also referred as hyphae. A complex group of filaments or hyphae is termed as mycelium. As the filaments increase the surface area of fungi, their basic function is to absorb nutrients from external sources. Enzymes for nutrient absorption are released by the filaments on the substrate and hence the nutrients are absorbed.