Inner Product of Polynomials: f(x) & g(x)

[grewas8]

Homework Statement

Define the inner product of two polynomials, f(x) and g(x) to be
< f | g > = ∫-11 dx f(x) g(x)
Let f(x) = 3 - x +4 x2.
Determine the inner products, < f | f1 >, < f | f2 > and < f | f3 >, where
f1(x) = 1/2 ,
f2(x) = 3x/2
and
f3(x) = 5(1 - 3 x2)/4
Expressed as a column vector these inner products are given by?


Can anyone help me understand this question, what is the point of g(x)? any help on approach would be helpful

 

[George Jones]

g is an arbitrary polynomial, so, g could be f1, g could be f2, etc.

 

[grewas8]

so do i just sub. f1 to find <f|f1> and take integral of f(x) and f1(x) ?

 

[VeeEight]

Yes, you just sub in the appropriate polynomials. So the first one will be < f | f1 > = ∫-11 dx f(x) f1(x) = ∫-11 (3 - x +4 x2) (1/2) dx