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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A: To find the inverse of the function f(x) = (x - 9)7 - 8, we need to express x in terms of y, where y…

Q: The functions f₁(x) = x² and f(x)=x³ are orthogonal on the interval [-3,3] ? True False

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Q: ) Is the function f(x) = differentiable on the open interval (-1,1)? x².

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Q: Determine the point at which the function is not analytic iz² – 2z ƒ(z) = 3z + 1 - i

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