For each of the following functions, determine whether the function is:Injective (one-to-one).Surjective (onto).⚫ Bijective.Justify your answers. 1.3 f: R→ ZZ such that f(x) = [4x] (i.e., ceiling of 4x).

First, to determine whether the function f : R→Z defined by f(x)=⌈4x⌉ is injective (one-to-one),…

Answered: For each of the following functions,…

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter13: Overloading And Templates

Section: Chapter Questions

Problem 30SA

See similar textbooks

Similar questions

In order for a function to be defined as a distance, it must provide certain properties (axioms). Accordingly, including J (.,.) Jaccard likeness, d (x, y) = 1-J (x, y) prove whether the function is a distance metric data mining
For each of the following ML functions, could the activation record for the function be deallocated as soon as the function returns? Explain why or why not. fun f x = fn y => y + 1 fun f x = map ~ x
Provide a counterexample to the statement: "Every function has its inverse function." Justify your answer.
(6a) how many different functions f : A → B can be defined if m=3 and n=5? (6b) if m=4 and n=6 then how many different one-to-one functions f : A →B can be defined? (6c) if m=5 and n=4 then how many different onto functions f : A → B can be defined?
So would this be a disprove, i.e. there is no such function?
justify whether each of the following functions is injective, surjective, bijective, or none of these categories: (N is the set of natural numbers, and Σ∗ is the set of all strings over Σ.) (a) h : Σ∗ → Σ∗, where Σ = {a, b}, and h(w) = wR
For each of the following functions, indicate the class (g(n)) the function belongs to. (Use the simplest g(n) possible in your answers.) Please show work to prove the assertions.
For each of the following ML functions, could the activation record for the function be deallocated as soon as the function returns? Explain why or why not. fun f x = x + 1 fun f x = fn y => x + y
Prove or disprove:(a)∃ sets A,B ∀ functions f: A→B, f is a bijection. (b) if f : A → B is a function, C ⊆ A, and D ⊆ B, then f : C → D is always a function.[Note 1: one is true, the other is false.][Note 2: feel free to draw bubble-arrow pictures here, but make sure you explain what’s going on very carefully.]
how many functions a) map {1,2,3.4.5.6} to {up,down,left,right} b) how many functions in part a are subjective? c) how many have f- inverse(up) =2
For the first problem, in parts b and c, how are the variables being taken from functions that they are not defined in? To clarify, in part c, how is the variable "b" taken from fun2 when it is not defined in that in function. Shouldn't the answer there just be "b(fun1)"
) Consider the following functions. Decide whether these functions are injective,surjective, and invertible. Justify your answer (e.g., if you claim that a function is invertible, you need togive a justification as to why you think that function is invertible). Give counterexamples when needed.You can draw arrow diagrams to help justifying your answer.a) Function f: ℤ × ℤ → ℤ is defined as f((a, b)) = 2b – 4a.b) A = {1, 2, 3}. Function f: ?(A) → {0, 1, 2, 3} is defined as f(X) = |X| where |X| = size of X. Forexample, |{1, 2}| = 2. ?(A) is the power set of A.c) Function f: {0, 1}3 → {0, 1}3 is defined by the following rule. For each string s ∈ {0, 1}3,f(s) = f(x1x2x3) = x3x1x2, where x1, x2, x3 ∈ {0, 1}. For example, if x1 = a, x2 = b, and x3 = c, thenf(abc) = cab. Another example: f(011) = 101.

SEE MORE QUESTIONS

Recommended textbooks for you

C++ Programming: From Problem Analysis to Program…

Computer Science

ISBN:

9781337102087

Author:

D. S. Malik

Publisher:

Cengage Learning