Consider the following piece-wise defined function (e is an unspecified constant). f(x)= - x+3 if x < 3 √x² + c if x ≥ 3 Find a value of e such that the function f(x) is continuous at x = 3. (5) Let f(x)= x³ + 2x - 2. (a) Use the Intermediate Value Theorem (stated below) to show that the equation f(x) = 0 has a solution in the interval (-1,1). (In other words, f had a root strictly between -1 and 1.) (b) What property of this function f allows us to use the Intermediate Value Theorem? (c) The Intermediate Value Theorem guarantees that the equation f(x) = 0 has at least one solution in the interval (-1,1). But in this case, it turns out that there is exactly one solution. How can you show that there is exactly one solution using other techniques from Calculus?