5) Let S = {1, 02, 03, 04} be an orthonormal set of functions on −1 ≤ x ≤ 1 using the usual inner products for functions. Suppose that functions f and g are given by f(x) = a11(x) + α202(x) + α303(x) + α404(x), g(x) = b₁₁(x) + b22(x) + b303(x) +b404(x). a) Show that (f, g) = a1b1 + a2b2+ a3b3 + a4b4. b) What does the result from a) remind you of?

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A: Solution :-

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A:

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A: For critical point:   Substitute,

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A: all the values which can be used as input in a function is called domain of a function

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A: If you have any questions let me know in comment box thankyou for your question.

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A: The first part of the question is asking us to prove that the sum of the kth powers of the first n…