1. Let X = {n eN:0 < n < 999} be the set of all numbers with three or fewer digits. Define the function f : X → N by f(abc) = a + b + c, where a, b, and c are the digits of the number in X (write numbers less than 100 with leading O's to make them three digits). For example, f(253) = 2 +5 + 3 = 10. (a) Let A = {n € X : 113 < n < 122}. Find f(A). (b) Find f-'({1,2}) %3D (c) Find f-1(3). (d) Find f-'(28). (e) Is f injective? Explain. (f) Is f surjective? Explain.
1. Let X = {n eN:0 < n < 999} be the set of all numbers with three or fewer digits. Define the function f : X → N by f(abc) = a + b + c, where a, b, and c are the digits of the number in X (write numbers less than 100 with leading O's to make them three digits). For example, f(253) = 2 +5 + 3 = 10. (a) Let A = {n € X : 113 < n < 122}. Find f(A). (b) Find f-'({1,2}) %3D (c) Find f-1(3). (d) Find f-'(28). (e) Is f injective? Explain. (f) Is f surjective? Explain.
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
Let X {n ∈ N : 0 ≤ n ≤ 999} be the set of all numbers with three
or fewer digits. Define the function f : X → N by f (abc) a + b + c,
where a, b, and c are the digits of the number in X (write numbers less
than 100 with leading 0’s to make them three digits). For example,
f (253) 2 + 5 + 3 10.
(a) Let A {n ∈ X : 113 ≤ n ≤ 122}. Find f (A).
(b) Find f
−1
({1, 2})
(c) Find f
−1
(3).
(d) Find f
−1
(28).
(e) Is f injective? Explain.
(f) Is f surjective? Explain.
Transcribed Image Text:14. Let X = {n e N :0 < n < 999} be the set of all numbers with three
or fewer digits. Define the function f : X → N by f(abc) = a + b + c,
where a, b, and c are the digits of the number in X (write numbers less
than 100 with leading O's to make them three digits). For example,
f(253) = 2+5+ 3 = 10.
(a) Let A = {n € X : 113 < n < 122}. Find f(A).
(b) Find f-1({1,2})
(c) Find f-'(3).
(d) Find f-1(28).
(e) Is f injective? Explain.
(f) Is ƒ surjective? Explain.
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