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## Homework Statement

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

## Homework Equations

## The Attempt at a Solution

I have solved part (a) and found that ll f ll = 1/2sqrt(e

^{2}+1) but I am having trouble with part B.

I see that the answer is b[x-(e

^{2}+1)/4] but I cannot get this answer. I know that (f, g) = 0 but I do not know how to solve this.