In the real linear space C(1, e), define an inner product by the equation (f,g) = integral(1 to e)(logx)f(g)g(x)dx.
(a) If f(x)=sqrt(x), compute ll f ll (the norm of f)
(b) Find a linear polynomial g(x)=a+bx that is orthagonal to the constant function f(x)=1
The Attempt at a Solution
I have solved part (a) and found that ll f ll = 1/2sqrt(e2+1) but I am having trouble with part B.
I see that the answer is b[x-(e2+1)/4] but I cannot get this answer. I know that (f, g) = 0 but I do not know how to solve this.