Final answer:
Sociologists may criticize the study of American culture because it is not a single, homogeneous entity but rather consists of multiple, often conflicting subcultures, reflecting a complex and dynamic societal landscape.
Step-by-step explanation:
When Lucy wants to study American culture, sociologists might be critical of such a study for several reasons. A commonly noted critique is that culture is not homogenous; thus, option c. suggests a valid critique stating that there is no single American culture, but rather a 'contested terrain of mainstream culture and hundreds, if not thousands, of subcultures.' This reflects the understanding that American society is incredibly diverse, with numerous cultural identities and perspectives, often leading to sociocultural conflicts and changes which make the study of 'American culture' complex.
Furthermore, sociologists stress the importance of recognizing the existence of both high culture and popular culture within societies, and the dynamic nature of cultures evolving over time through invention or discovery. There is also an ethical consideration regarding the representation in cultural research, as American culture is not unique in its complexity, and includes multiple identities that a single researcher might not fully grasp or represent. Therefore, the critical nature of sociological inquiry is essential in providing a holistic, informed perspective on American culture, taking into account all its complexities and nuances.