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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.

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.

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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Let X = {neN: 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 ƒ(A). (b) Find ƒ-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:Let X = {neN: 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 ƒ(A). (b) Find ƒ-¹({1,2}) (c) Find f-¹(3). (d) Find f-¹(28). (e) Is f injective? Explain. (f) Is f surjective? Explain.
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