Let R denote the set of continuous functions with domain R (as in calculus). Then R...

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Let R denote the set of continuous functions with domain R (as in calculus). Then R is a commutative ring with identity. The additive identity OR is the zero function (that is, the function h(x) which is zero at every point). 1. Let S denote the set of polynomial functions. Show that S is a subring of R. 2. Let [x if x ≥ 0 10 if x < 0. Let g(x) = f(-x). What is the function f(x) g(x)? 3. Is R an integral domain? Justify your answer. 4. Is S an integral domain? Justify your answer. (You may use the fact that a polynomial of degree n has at most n roots.) f(x) = Let R denote the set of continuous functions with domain R (as in calculus). Then R is a commutative ring with identity. The additive identity OR is the zero function (that is, the function h(x) which is zero at every point). 1. Let S denote the set of polynomial functions. Show that S is a subring of R. 2. Let [x if x ≥ 0 10 if x < 0. Let g(x) = f(-x). What is the function f(x) g(x)? 3. Is R an integral domain? Justify your answer. 4. Is S an integral domain? Justify your answer. (You may use the fact that a polynomial of degree n has at most n roots.) f(x) =