
Lois P. answered 06/25/19
English Expertise - 3 Years of ESL and Tutoring
To quote the Cambridge English dictionary, which I consider a "go to" source for any questions I have while teaching English class, the above example is correct. One can say "No, I'm not tired. Rather the opposite in fact." Here we see two sentences with a period separating them, not a semicolon. The second sentence is just an added remark about the first sentence. The word "rather" is being used to emphasize the fact that the speaker really is not tire in the least.