(2) Fix an interval [a, b]. Let C[a, b] be the set of continuous functions from [a, b] to R. For f,g€ C[a, b], define a dot product and norm by
f.g:=∫ f(x)g(x)dx, ||f||2:= √f.f = (∫ |f(x)|2 dx)1/2
(note the absolute value is actually not necessary). The dot product is clearly bilinear and symmetric (you do not need to show this or that defines a dot product). Show that 2 is a norm on C[a, b].