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(a) Let f : Z × Z → Z be the function f(m, n) = m²n + n. Is f one-to-one? Is f onto? Justify your answer. (b) Let f : N –→ N be the function f(n) = 2n + 2. Is ƒ one-to-one? Is f onto? Justify your answer.

(a) Let f : Z × Z → Z be the function f(m, n) = m²n + n. Is f one-to-one? Is f onto? Justify your answer. (b) Let f : N –→ N be the function f(n) = 2n + 2. Is ƒ one-to-one? Is f onto? Justify your answer.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(a) Let f : Z × Z → Z be the function f(m, n) = m²n + n. Is ƒ one-t0-one? Is f onto? Justify your answer. (b) Let f : N –→ N be the function f(n) = 2n + 2. Is f one-to-one? Is f onto? Justify your answer. (c) Let f(x) = x³ + 2x + 1, g(x) = sin x, h(x) = x² + 2. Write down explicitly the formulas for (h ogo f)(x) and (fogoh)(x).
Transcribed Image Text:(a) Let f : Z × Z → Z be the function f(m, n) = m²n + n. Is ƒ one-t0-one? Is f onto? Justify your answer. (b) Let f : N –→ N be the function f(n) = 2n + 2. Is f one-to-one? Is f onto? Justify your answer. (c) Let f(x) = x³ + 2x + 1, g(x) = sin x, h(x) = x² + 2. Write down explicitly the formulas for (h ogo f)(x) and (fogoh)(x).
(a) Let A, B, C be sets. Show the set identity (AnC)-(BNC) = (AnB)-C. (b) For a set A denote P(A) the power set of A. Write explicitly the set P(P(P(Ø)))?
Transcribed Image Text:(a) Let A, B, C be sets. Show the set identity (AnC)-(BNC) = (AnB)-C. (b) For a set A denote P(A) the power set of A. Write explicitly the set P(P(P(Ø)))?
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