Let X = {n € N : 0≤ n ≤ 999} be the set of all numbers with three or fewer digits. Define the function ƒ : 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). In other words, f returns the sum of the digits of its input. For example, f(253) = 2+5+3 = 10. a. Let A = {n € X : 308 ≤ x ≤ 325}. Find f(A). {4,5,6,7,8,9,10,11,12 b. Find f-¹({1,3}) {1,10,100,120,102,12 c. Find f-¹(2). {2,11,20,101,110,20C d. Find f-¹(287).
Let X = {n € N : 0≤ n ≤ 999} be the set of all numbers with three or fewer digits. Define the function ƒ : 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). In other words, f returns the sum of the digits of its input. For example, f(253) = 2+5+3 = 10. a. Let A = {n € X : 308 ≤ x ≤ 325}. Find f(A). {4,5,6,7,8,9,10,11,12 b. Find f-¹({1,3}) {1,10,100,120,102,12 c. Find f-¹(2). {2,11,20,101,110,20C d. Find f-¹(287).
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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Transcribed Image Text:Let X = {n EN: 0≤ n ≤ 999} be the set of all numbers with three or fewer digits.
Define the function ƒ : 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). In other words, f returns the sum of the digits of its input. For example,
f(253) = 2+5+ 3 = 10.
a. Let A = {n € X : 308 ≤ x ≤ 325}. Find f(A).
{4,5,6,7,8,9,10,11,12
b. Find f-¹({1,3})
{1,10,100,120,102,12
c. Find f-¹(2).
{2,11,20,101,110,20C
d. Find f ¹(287).
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