6. Use the fact that every odd degree polynomial with real coefficients has a real root to show that the function f : R –R defined by ƒ (x) = x³ – 2.x² + x for x ER is onto. Is f one-to-one? Bonus: Let A = {a,b, c} be a set and P(A) be the power set of A. Define f : P(A) → Z by the rule f (A) = number of elements of A. Is f one-to-one? If so, prove it. Otherwise, give an counterexample.

Q: Give the domain of the function. z = 4x – 5y O {(x, y): x and y are real and 4x – 5y = 0} O {(x, y):…

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Q: Q2: (a) Determine which of these functions are injective, surjective, and bijective. The function f…

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Q: Viewed as a function f: R → R, a polynomial of odd degree is always surjective. True False

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Q: d) Let the set A = {1,2,3,4} and let P(A) denote the power-set of A. Consider the following…

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Q: let a= {0,4,9,1.6} , b={0,3,6,12,20} and f a function. from a to b with f(x)=√x + x. A. Find f(0),…

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Q: Viewed as a function f: R → R, a polynomial of even degree is never injective. True False

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Q: Let X = the integers. Let Y = {0, 1, 2, 3, 4, 5}. %3D Let f : X Y be defined as the remainder when x…

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Q: ) Prove that, if a and b are nonnegative integers such that a =4 b, then 3ª =5 3b. Using (a),…

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Q: Express the function F in the form f∘g. (Enter your answers as a comma-separated list. Use…

A: Remark: we know that (f•g)(x) = f(g(x))

Q: (a) Prove that, if a and b are nonnegative integers such that a = 4 b, then 3ª =5 3b. (b) Using (a),…

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Q: . Let ƒ(x) = (x² - 4)³. Do the following. (a) Find the maximum value and the minimum value of f on…

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