3. Define f(x) so that S(2) = {ap(). f(x) = 0, |피 <1 |r| > 1 (a) Explain why the function f(x) must be continuous everywhere except perhaps at r = ±1. Hint: How is f(x) constructed from known continuous functions? (b) State the definition for f(r) to be continuous at c. Assume that c is not an endpoint. (c) Prove that f(x) is in fact continuous at both –1 and 1. (d) State the limit definition for f(x) to be differentiable at c. Assume that c is not an endpoint. (e) Explain why the function f(x) must be differentiable everywhere except perhaps at r = ±1. Hint: How is f(x) constructed from known differentiable functions? (f) Prove that f(r) is in fact differentiable at both -1 and 1.