Consider the vector space C[0,1] with inner product$ 0 ∫ 1 $f(x)g(x) dx .

(a) Determine whether the function f(x)=3x is a unit vector in this space. If it is, then show that it is. If it is not, then find a function that is.

(b)Find in exact form the cosine of the angle between f(x)= 5x^2 and g(x)=9x.