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

  1. Oct 7, 2014 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations

    3. 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.
     
  2. jcsd
  3. Oct 7, 2014 #2

    mfb

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    2016 Award

    Staff: Mentor

    Did you apply the definition of the inner product to this equation? Then you can solve it and get conditions for a and b.
     
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