Please answer True or False for the following Statements... 1. For all integers n, if n^3 -n +1 is even then N^3 -n + 3 is odd (Would be True because False Hypothesis right? Cause would never be even for initial statement.) 2. Let f: R->R be f(x) = x^2 -x + 1. Then f is an injection (Confused on what this problem is saying such as with f: R->R) 3. Let f: A->B be a bijection. Then f^-1: B ->A is bijection. (Is this true as if original function is a bijection then so too is the inverse? Right?)

Please answer True or False for the following Statements... 1. For all integers n, if n^3 -n +1 is even then N^3 -n + 3 is odd (Would be True because False Hypothesis right? Cause would never be even for initial statement.) 2. Let f: R->R be f(x) = x^2 -x + 1. Then f is an injection (Confused on what this problem is saying such as with f: R->R) 3. Let f: A->B be a bijection. Then f^-1: B ->A is bijection. (Is this true as if original function is a bijection then so too is the inverse? Right?)

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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Question

Please answer True or False for the following Statements...

1. For all integers n, if n^3 -n +1 is even then N^3 -n + 3 is odd

(Would be True because False Hypothesis right? Cause would never be even for initial statement.)

2. Let f: R->R be f(x) = x^2 -x + 1. Then f is an injection

(Confused on what this problem is saying such as with f: R->R)

3. Let f: A->B be a bijection. Then f^-1: B ->A is bijection.
(Is this true as if original function is a bijection then so too is the inverse? Right?)

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