What is the appropriate response to: "Doesn't your cat like _____?"?

The appropriate response in this context is "to be stroked" because it correctly follows the structure of the question, which implies a passive construction. The phrase "Doesn't your cat like" indicates that we are talking about something the cat enjoys receiving rather than something it does actively. "To be stroked" communicates that the cat enjoys being petted or touched, emphasizing the action performed on the cat.

Using "stroked" would be grammatically incorrect in this structure, as it lacks the necessary "to be" for a complete thought about the cat's preferences. "Stroking" would suggest an ongoing action, which doesn't fit the question's intent. Lastly, "stroke" implies a noun or a command and does not convey the intended meaning of the action being performed on the cat.

Thus, "to be stroked" is the only choice that fits both linguistically and contextually, making it the best answer.