Let f be some continuous function on an open interval I containing x0, x1 and x2, where xo < x1 < x2. Suppose that (xo, yo), (x1, Y1) and (r2, y2) are points on the curve y =f(x). Let a E (x, x1) and P(x) the polynomial interpolating to f at Xi, i = 0,1, 2. a) The degree of P(x) can be at most

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Q: 1. Describe all functions f such that f(r) ar² + bx +c and f(1) = 2 and f(-1) = 6.

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A: To prove that the given linear function is continuous.

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Q: Let f be some continuous function on an open interval I containing x0, x1 and x2, where xo <x1 <x2.…

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Q: Let f: Z → Z be defined by f(x) = x² + 1, and let C = {1,2,3}.

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Q: Suppose f: R → R is a function defined by f(x) = x³. (a) Find f([-1,1]) and f-¹([0, 8]). (b) Show…

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Q: 5. Show that the functions x, x² interval [-1,1]. x are mutually orthogonal in the -

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Q: Show that f : ℝ → ℝ, f(x) = 5x − 3 is a bijective function.

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Q: Exercise 2. Let f : A → B be a function with Y1 and Y2 subsets of B. Prove that if Y1 C Y2, then…

A: Let f:A→B be a function and let Y1,Y2⊆B. Suppose that Y1⊆Y2 To show f-1(Y1)⊆f-1(Y2) Let x∈f-1(Y1)…