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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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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