• Support PF! Buy your school textbooks, materials and every day products Here!

Find a g=a+bx that is orthagonal to the constant function

  • Thread starter Cassi
  • Start date
  • #1
18
0

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(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.
 

Answers and Replies

  • #2
34,364
10,434
I know that (f, g) = 0 but I do not know how to solve this.
Did you apply the definition of the inner product to this equation? Then you can solve it and get conditions for a and b.
 

Related Threads on Find a g=a+bx that is orthagonal to the constant function

Replies
7
Views
10K
  • Last Post
Replies
3
Views
832
  • Last Post
Replies
1
Views
945
  • Last Post
Replies
1
Views
849
  • Last Post
Replies
2
Views
3K
Replies
12
Views
3K
  • Last Post
Replies
2
Views
7K
  • Last Post
Replies
1
Views
606
Replies
4
Views
2K
  • Last Post
Replies
5
Views
1K
Top