9. Determine whether f is injective, surjective or bijective.a. Suppose f: N→ N has the rule f(n) = 4n+ 1.b. Suppose f: Z → Z has the rule f(n) = 3n² – 1.c. Suppose f:Z-Z has the rule f(n)-3n-1.d. Suppose f : N → N has the rule f(n) – 4n² + 1.e. Suppose f: R → R where f(x) = [x/2].

Answered: Image /qna-images/answer/cabeeb3d-994c-43a3-a3e1-834d9a5ee1df.jpg

Answered: 9. Determine whether f is injective,…

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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Consider the given predicate functions. P(n): "n is a prime number" E(n): "n is an even number" P and E both have domain = {nZ:n>1} Identify the TRUE statement(s). Explain your answer. I. En(E(n)^P(n)) II. Vn(E(n)VP(n)) III. \n(→E(n)→ P(n)) IV. En(-P(n)→→E(n)) O II only O I only O I and II only O II and III only O III only O I and IV only SO IV only O none
I want to check my answers on a and b. as for c and di, how would i find the solution? Letf(x)=3–x andg(x)=x–3. a. Evaluate f (2) and g (2). b. Evaluate f (–2) and g (–2). c. Which function, f or g, has the domain (– ∞, ∞)? d. Which function, f or g, can have negative function values?
What is the end behavior of the given function? f (x) = -2/x+1+4 O As x → 0, f(x) → 4. As x → -1, f(x) → o. O As x → o, f(x) → -∞. As x → –1, f(x) → 4. O As x → o, f(x) → 4. As x → -1, f(x) → -0o. As x → 0, f(x) → o. As x → –1, f(x) → 4.
Show directly that f(n) = n² + 3n³ € (n³). That is, use the definitions of O and Q to show that f(n) is in both O(n³) and (n³).
13. (9 points) Let D be the set of finite subsets of positive integers. Let S be the set of all positive integers greate than or equal to 2. Define a function T:S → D as follows: For each integer n ≥ 2, T(n) = the set of all even factors of n. a) Find T(10). b) Find T(17) c) Find T(m), where m is any odd positive integer.
2. Let f(x) = 3x – 7, find a linear function g for which f (g)= I and for which f(g (x)) =x for any number x the function g is: a. g:x →+7. 3 x+7 b. g:x→- 3 7-x c. g:x→ 3 x+7 d. g:x→- 3 x-7 e. g:x→ 3

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