X7.) Let f: N→ Z with f(n) = n+4. Let A = {1,2,3} and B = {z € Z \ I < 10).Use these to find the following sets.(a) An B(b) P(A\ {1, 2}) × A(c) f(A)(d) f-¹(B)4112=170f(0)

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Answered: 7. ) Let f: N→ Z with f(n)=n+4. Let A =…

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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3. Let the function f :R → R be defined as follows: (3х-1 if x>3 f (x)={x² – 2 if - 2
3. Let f A B be a function, and let Ao C A, BoC B. Prove that (a) f(f(f(Ao))) = f(Ao); (b) f(f(f¹(Bo))) = f-¹(Bo).
4) i) Let f: N→ C be a function with f(30) = 0, f(70) = 1 and f(105) = 1. Determine whether f is multiplicative or not. Explain why. Show that f(1) = 0 or f(1) = 1 if f is multiplicative. Determine whether the following functions are multiplicative or not. Give a detailed ii) iii) explanation. a) f(n)= ^ 1 if n 1 mod (2) 2 if n2 mod (2) b) f(n) = 1 if n 1 2 if n2 3 if n 0 mod (3) mod (3) mod (3)
(2) Consider the claim: (Vx E N)(3 y E R)P(x, y) = (3 y e R)(Vx E N)P(x, y). (2.1) What is the domain of the predicate P(x, y)? (2.2) Give an example of a predicate P(x, y) for which the above claim is true. (2.3) Give an example of a predicate P(x, y) for which the above claim is false.
The function f(x) = 8x – x² is increasing on : A. (-00, 4). B. [4,0). C. [0, 8]. D. [-8, 0]. Select one: O A O D O B O C
Define f: [0,2]-R by f(x) = x²+2x-1 , then the sup f- inf f is : [0,2] [0,2) .a | .b 8 .C 8, .d 1 3.
1 2 (a) Find A- if A = 2 3 (b) Find values of x and y such that r 2. +y
For the function f given by S(z) = 32 +3 evaluate f(z + h) – f(z) a) 06h +3z b) 0-6h +3r c) 06h + 6z d) 03h + 6z e) O-3h + 6z f) ONone of the above
5. Let f, and f, be the function from R to R such that f,(x) = x²+2x+3 and f2(x) = x-x? . What are the functions f,+f, and f,f;?
Let f: P(N) → P(N) be the f(X) =X∪{8,9} defined function. 1)What is the value when f({6,8})? 2) what is the relationship of f 3)The image of f is? Choose one A) N B) P(N) C) P({8,9}) D) {8,9} E) {X:X∈ P(N) and {8,9}⊆ X} F) All is wrong
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For what sets X and Y is the function f: X Y defined by 3x f (x) = x +4 a bijection?

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7. ) Let f: N→ Z with f(n)=n+4. Let A = {1,2,3} and B = {1 € Z \ I <10). Use these to find the following sets. (a) An B (b) P(A\ {1,2}) × A (c) fƒ(A) (d) f-¹(B) 5/12 - 10