Could someone please check my work and let me know if it's correct

A function f : R - R is periodic if there exists a real number k > 0 so that f(x + k) = f(a) for all TER. 1. Give an example of a periodic function g: R - R. (The function should not be a constant function). Justify your answer. 9 2 (6 ,a ) bas zuountinos at Any of the trigonometric functions are periodic functions. For example, sin (x) is a periodic function with period, 27 that repeats in even multiples of 7 , so it follows the above y br construction of a periodic function where k = 2n7 > 0: f(x + k) = sin(x + 2n7) = sin(x) = f(x) for all n E N where k = 2nT > 0 carb ard ed son daugh It .zum Insignes s