In the real linear space C(-1, 1) with inner product (f, g) = integral(-1 to 1)[f(x)g(x)]dx, let f(x) = ex and find the linear polynomial g nearest to f.
The Attempt at a Solution
I understand that the best approximation for g is equal to the projection of f. Therefore, in order to find the linear polynomial g nearest to f, I must calculate this projection. However, I do not know how to solve for the projection.
(The solution in my book is g(x) = 1/2(e-e-1) + (3/e)x)