Consider the inner product of two functions defined by {ƒ, g) = f w(x) f(x)g(x) dx a where w(x) is a weight function. (a) Show the set of the functions {1, x, 5x² - 1} is orthogonal with re- - spect to the weight function w(x) = 1 − x² on the interval [−1, 1]. (b) Make the set an orthonormal set of functions.

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