(c) Prove that every function f(x) can be written as a sum of an even function and an odd function. For any function f with domain R, define functions E(x) = f(x) + f(-x) and O(x) = f(x)-f(-x), as in parts (a) and (b). Then answers completely.) - E(X) + 10(x) = [(x) + f( [₁0+1 (2x)] )] + 1/[(*)-(-)] ])) + (²x) - ((-x)] O f(x) = (d) Using parts (a), (b), and (c), express the function f(x) = 2*+ (x - 3)2 as a sum of an even function and an odd function. =1/√(2x + x + (x − 3)² + 2x + (x + 3)²) + (2x + (x − 3)² - 2* - (x + 3)²) O Rx) = (2x + (x-3)² - 2x - (x + 3)²) + (2x + (x − 3)² - 2* — (x + 3)²) O f(x) = (2x + (x-3)² + 2* + (x + 3)²) - ¹½ (2* + (x − 3)² – 2x − (x + 3)²) Of(x) = (2x + (x-3)² + 2*+ (x+3)²) - (2x + (x-3)² - 2x - (x + 3)²) O Rx) = (2x + (x-3)² -2°* - (x + 3)²) + ½ (2* + (x − 3)² - 2¯* - (x + 3)²) O f(x) = (2x + (x-3)² + 2¯* + (x + 3)²) + (2* + (x − 3)² - 2-* - (x + 3)²) Eis -Select- 0 is Select, and we show that f(x)=E(x) +10(x). (Simplify your

Suppose the rule of the function f is "add one" and the rule of the function g is "multiply by 4." How can we express these functions algebraically? f(x) = g(x) = (f o g)(x) = (g o f)(x) =