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Let f and g be functions from A to B. Decide, with reasons, whether the functions are (i) one-to-one; (ii) onto. A (B) A = R, B = [0, ∞): f(a) = 2a. A = B = R: g(a) a² - 1 3

Let f and g be functions from A to B. Decide, with reasons, whether the functions are (i) one-to-one; (ii) onto. A (B) A = R, B = [0, ∞): f(a) = 2a. A = B = R: g(a) a² - 1 3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Topic: Discrete Mathematics

Let f and g be functions from A to B. Decide, with reasons, whether the functions are (i) one-to-one; (ii) onto. A B A = R, B = [0, ∞): f(a) = 2a. A = B = R: g(a) a² - 1 3 Use the definition of O(f) to show that n² is O(n² log n). Is n² log n also O(n²)? Prove your answer.
Transcribed Image Text:Let f and g be functions from A to B. Decide, with reasons, whether the functions are (i) one-to-one; (ii) onto. A B A = R, B = [0, ∞): f(a) = 2a. A = B = R: g(a) a² - 1 3 Use the definition of O(f) to show that n² is O(n² log n). Is n² log n also O(n²)? Prove your answer.
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