14. 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({1,2}) %3D (c) Find f-1(3). (d) Find f-1(28). (e) Is f injective? Explain. (f) Is f surjective? Explain.

14. 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({1,2}) %3D (c) Find f-1(3). (d) Find f-1(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

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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