Let f: R+→ N+ with f (x) = [x²]; that is, f(x) returns the square of x rounded up. Characterize f in terms of whether it is injective, surjective and/or bijective. This is not a formal proof, but briefly explain your reasoning. %3D

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Q: Find the constant a, or the constants a and b, such that the function is continuous on the entire…

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Q: (a) Verify Rolle's Theorem for f(x)= 3x – 12.x + 4 over the interval 0, 2

A: Verify rolle's theorem

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Q: (b) Use the definition in (a) to compute f'(2) for the function f(x)

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Q: Describe the long run behavior of f(2) = - z As z + - 00, f(z) + ? As a + 00, f(æ) → ?

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Q: Let f(x) = 4 – a?, a > 0 f- (x) =

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Q: Consider the function h : N → N given by h(n) = n + (-1)"+'. 1. Is h surjective? 2. Is h injective?

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Q: . Consider the function f : Z x Z → Z x Z defined by f(a, b) = (a+ b, a - b). %3! Is f injective? Is…

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Q: let f(x) = on interval 0<x<2n, find a 2

A: See the attachment

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Q: Use the IVT to show that f(x) = x 3 + x takes on the value 9 for some X in [1, 2].

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Q: Find the constant a such that the function is continuous on the entire real line. x² - a² if x * a…

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