How many functions f: {1, 2, 3, 4} → {1, 2, 3, 4} are there satisfying:a. f(1) = 1 or f(2)= 2 (or both)?b. ƒ(1) ‡ 1 or ƒ(2) ‡ 2 (or both)?c. ƒ(1) ‡ 1 and ƒ(2) ‡ 2, and ƒ is injective?d. f is surjective, but Vx = {1, 2,...,4}, ƒ(x) ‡ x?JI-FI-

Answered: How many functions f: {1,2,3,4}…

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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2. The function f and g of the real variable x are defined as; x +x-2 and f:x> g:x 3x+2 x+4 i. State the domain of each function ii. Show that g(a) = g(b)%3Da%3Db What conclusion can you draw from this result? State the zeros of the functionf iii. iv. Find fog (3)
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How many functions f: {1,2,3,4} {1,2,3,4} are there satisfying: a. f(1) = 1 or f(2)= 2 (or both)? b. f(1) # 1 or f(2) # 2 (or both)? c. ƒ(1) ‡ 1 and ƒ(2) ‡ 2, and ƒ is injective? d. f is surjective, but Va E {1,2,...,4}, f(x) = x? A A J F