Show by explicit computation that S(2ex) 2s(ex). Is S linear? For the transformation S in part(c),find two functions f and g, f g, such that S(f+g) S(f) + S(f). Let U be defined by U(f) = 1 -1 xf(x)dx Is U linear? Let C([-1,1]) be the vector space of continuous functions on the interval [-1,1] and define T: C ([-1,1]) rightarrow R by T(f) = 1 -1 f(x) dx Thus, for example, T(x3) = 1 -1 x3 dx = x4/4 1 -1 = 0 Let f(x) = ex and g(x) = x2 for -1