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Suppose f:N→ N has the rule f(n) = 3n² – 1. (a) Determine whether f is surjection onto N and show why. (b) Determine whether f is injection into N and show why.

Suppose f:N→ N has the rule f(n) = 3n² – 1. (a) Determine whether f is surjection onto N and show why. (b) Determine whether f is injection into N and show why.

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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Suppose f: N→ N has the rule f(n) = 3n² – 1. (a) Determine whether f is surjection onto N and show why. (b) Determine whether f is injection into N and show why.
Transcribed Image Text:Suppose f: N→ N has the rule f(n) = 3n² – 1. (a) Determine whether f is surjection onto N and show why. (b) Determine whether f is injection into N and show why.
Use the Principle of Mathematical Induction to prove that n > n? +3 for all n> 2.
Transcribed Image Text:Use the Principle of Mathematical Induction to prove that n > n? +3 for all n> 2.
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