4. Suppose f: Z-Z has the rule f(n)= 3n2-1. Determine whether f is one-to-one. 5. Suppose f: N-N has the rule f(n)= 4n2+1. Determine whether f is onto N.
4. Suppose f: Z-Z has the rule f(n)= 3n2-1. Determine whether f is one-to-one. 5. Suppose f: N-N has the rule f(n)= 4n2+1. Determine whether f is onto N.
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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4 & 5 ONLY.
![4. Suppose f: Z-Z has the rule f(n)= 3n2-1. Determine whether f is one-to-one.
5. Suppose f: N-N has the rule f(n)= 4n2+1. Determine whether f is onto N.
6. Suppose f: R→R where f(x)=[x].
a. If S = {x|1 ≤x≤ 6), find f(S).
b. If T=(3,4,5), find f-1(T).
7. Suppose g: A→ B, and f: B→ C where A = {1, 2, 3, 4), B = {a,b,c}, C=(2, 8, 10), and g and fare
defined by g = {(1, b), (2, a), (3, b), (4, a)} and f = {(a, 8), (b, 10), (c, 2)}.
a. Find fog
b. Find f-1
c. Find fo f-1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa52e5c13-ae63-4c89-8471-0652135b05c7%2F918af43b-5bb6-45e7-a0f2-a650925dfd12%2Fdyrsszb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Suppose f: Z-Z has the rule f(n)= 3n2-1. Determine whether f is one-to-one.
5. Suppose f: N-N has the rule f(n)= 4n2+1. Determine whether f is onto N.
6. Suppose f: R→R where f(x)=[x].
a. If S = {x|1 ≤x≤ 6), find f(S).
b. If T=(3,4,5), find f-1(T).
7. Suppose g: A→ B, and f: B→ C where A = {1, 2, 3, 4), B = {a,b,c}, C=(2, 8, 10), and g and fare
defined by g = {(1, b), (2, a), (3, b), (4, a)} and f = {(a, 8), (b, 10), (c, 2)}.
a. Find fog
b. Find f-1
c. Find fo f-1
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