Could someone please check my work

Theorem 5.2.10 Let f and g be functions from D to R , and let c E D . Suppose that f and g are continuous at c. Then (a) f + g and fg are continuous at c , and (b) - is continuous at c if g(c) # 0. g Theorem 5.4.6 Suppose f : D - R is continuous on a compact set D . Then f is uniformly continuous on D. Let f and g be real-valued functions that are uniformly continuous on D , and suppose that g(x) * 0 for all & E D. Assume I= " is uniformly continuous on D= [2, 5]. Prove That if D is compact, Then - Must be uniformly continuous on D. 1 Find am now Since - is continuous by Theorem 5.2.10, then by Theorem 5.4.6, since is g continuous on compact set, D = [2, 5] as evidenced in problem one part one of this homework assignment, then - is uniformly continuous on D . g