consider functions f: {1,2,3} -> {1,2,3,4}  a. how many functions are there total b. how many functions are injective c. how many of the injective functions are increasing

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Q: (a) Let n and k be non-negative integers. Explain what the function pr(n) counts.

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Q: 8. Let the functions f: A → B, g:B → C,h: C → D be defined by the figure below. A B h D 3 a. Which…

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Q: show that A0 subset f-1 (f(A0)) and that equality holds if f is injective

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Q: Find the domain of the function.

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Q: Suppose f : A → B is an injective function, and {A;};e1 is a partition of A. Prove that {F (A;)};er…

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Q: Define a function S: Z+ → Z+ as follows. For each positive integer n, let S(n) = the sum of the…

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Q: Consider the possible functions from [7] to [9].  How many in which f-1 is not a functio

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Q: 7. Let f (z) be an entire function with |f(z)|< C[z| for all z, where C is a constant. Show that f…

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Q: How many one-to-one functions f:[4] to [6] have 5 not in the rng(f)?

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Q: the function f, evaluate f(−6), f(−5), f(−1), and f(0). f(x) =    x + 4   if   x < −5 −2x − 1   if…

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Q: the functionf is shown in the figure below. nd range of f as intervals or unions of intervals.

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Q: a real valued function in [a, b] such that f(x) is different in A. (a, b) B. [a,b C. (a,b] D. [a, b)

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Q: A function f(x) is given by the following set of ordered pairs: {(2,6), (4, 12), (5, 15), (9, 27)}.…

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Q: Consider sets A and B with |A| = 8 and |B| = 21. %3D a. How many functions f: A → B are there? b.…

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Q: Use the graph of f to find the largest open interval on which f is increasing, and the largest open…

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Q: Let S be the set of monotone increasing functions { f:N → N | Vx < x' € N, ƒ (x) < f(x') } What is…

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Q: :N→N defined by n - the sum of thed

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Q: 6. Based on what you know about the multiplicative principle, how many functions f:A- Bare there if…

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Q: (a) Let f: [a, b] - Show that fE R([a, b)). R be abounded monotonic deczeasing function.

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Q: Consider functions f:{1,2,3,4} → {a, b, c}. a. How many functions are there? b. How many functions…

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Q: 3. In each part, find a function f : N → N that has the desired properties. (i) Surjective, but not…

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Q: Let f be a multiplicative function. Examine whether F(n) = [Idn f(d) is multiplicative

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Q: Consider a function f : N x N → N given by f(x, y) = 3"7ª. For what natural n, 21 · 57-3 is in the…

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