Could someone please check my work

Please state all definitions and theorems that you will need: Thearea 5.4He Suppose of: D ->Ro is continuous on a compact set is . Then of is uniformly continuous on D. for all a E R . A function f: R -+ R is said to be periodic if there exists a number k > 0 such that f(x + k) = f(x) Suppose that f : R - R is continuous and periodic. Prove that f is bounded and uniformly continuous on R . Suppose That file -R is continuous and periodic. Consider The periodic function g: 50, K]-+ PRO, 9(x) = f(x)= f(x+K). Since [0, K] is a closed and bounded interval, q is bounded on Co, K] and Thus uniformly continuous or This restricted interval by Theorem 5.4.6. To show that of is uniformly continuous on FR: Leq ESO. Then 7850 9 (gla)-g ( 6)/