The functional determinant of
x, e^x, and e^-x is equal to??
See:
http://en.wikipedia.org/wiki/Wronskian
To find the functional determinant of the given functions x, e^x, and e^-x, we need to represent them as a matrix.
Let's denote the functions as f_1(x) = x, f_2(x) = e^x, and f_3(x) = e^-x.
The matrix representation of these functions will have three rows where each row represents the value of the corresponding function at a particular point. In this case, we assume that the functions are evaluated at x = 0.
So, the matrix representation M will be:
M = |f_1(0) f_2(0) f_3(0)| = |0 1 1|
To compute the functional determinant, we find the determinant of matrix M. In this case, it is simply:
det(M) = 0 * (1/e^0) * (1/e^0) = 0.
Therefore, the functional determinant of x, e^x, and e^-x is equal to 0.