Question

Which of the following are one-to-one, onto, or both? a. f : Q → Q defined...

Which of the following are one-to-one, onto, or both?
a. f : Q → Q defined by f(x) = x3 + x.
b. f : S → S defined by f(x) = 5x + 3.
c. f : S → S defined by:

?(?) = {
? + 1 ?? ? ≥ 0
? − 1 ?? ? < 0 ??? ? ≠ −10
? ?? ? = −10

d. f : N → N × N defined by f(n) = (2n – 1, n).

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove: If D = Q\{3}. R = Q\{-3}, and f:D-> R is defined by f(x) =...
Prove: If D = Q\{3}. R = Q\{-3}, and f:D-> R is defined by f(x) = 1+3x/3-x for all x in D, then f is one-to-one and onto.
3. For each of the piecewise-defined functions f, (i) determine whether f is 1-1; (ii) determine...
3. For each of the piecewise-defined functions f, (i) determine whether f is 1-1; (ii) determine whether f is onto. Prove your answers. (a) f : R → R by f(x) = x^2 if x ≥ 0, 2x if x < 0. (b) f : Z → Z by f(n) = n + 1 if n is even, 2n if n is odd.
1. A function f : Z → Z is defined by f(n) = 3n − 9....
1. A function f : Z → Z is defined by f(n) = 3n − 9. (a) Determine f(C), where C is the set of odd integers. (b) Determine f^−1 (D), where D = {6k : k ∈ Z}. 2. Two functions f : Z → Z and g : Z → Z are defined by f(n) = 2n^ 2+1 and g(n) = 1 − 2n. Find a formula for the function f ◦ g. 3. A function f :...
Suppose f: R^2--->R is defined by f(x,y) = 3y. Is f one-to-one? Is f onto? Is...
Suppose f: R^2--->R is defined by f(x,y) = 3y. Is f one-to-one? Is f onto? Is f a bijection?
Let ?: ℝ → ℤ be defined as ?(?) = ⌊?⌋. a.) Is f one-to-one? b.)Is...
Let ?: ℝ → ℤ be defined as ?(?) = ⌊?⌋. a.) Is f one-to-one? b.)Is f onto? c.) Is f a bijection? d.)How would your answers change if ℝ is changed to ℤ?
Give an example of (a) a function f : Z → N that is both one-to-one...
Give an example of (a) a function f : Z → N that is both one-to-one and onto N; (b) a function f : N → Z that is onto Z and not one-to-one
Let X=2N={x=(x1,x2,…):xi∈{0,1}} and define d(x,y)=2∑(i≥1)(3^−i)*|xi−yi|. Define f:X→[0,1] by f(x)=d(0,x), where 0=(0,0,0,…). Prove that maps X onto...
Let X=2N={x=(x1,x2,…):xi∈{0,1}} and define d(x,y)=2∑(i≥1)(3^−i)*|xi−yi|. Define f:X→[0,1] by f(x)=d(0,x), where 0=(0,0,0,…). Prove that maps X onto the Cantor set and satisfies (1/3)*d(x,y)≤|f(x)−f(y)|≤d(x,y) for x,y∈2N.
Determine which of the following functions are injective (one-to-one) on their respective domains and codomains (a)...
Determine which of the following functions are injective (one-to-one) on their respective domains and codomains (a) f : ℝ → [0,∞), where f(x) = x² (b) g : ℕ → ℕ, where g(x) = 3x − 2 (c) h : ℤ_7 → ℤ_7, where h(x) ≡ 5x + 2 (mod 7) (d) p : ℕ ⋃ {0} → ℕ ⋃ {0}, where p(x) = x div 3
Let S = {A, B, C, D, E, F, G, H, I, J} be the set...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set consisting of the following elements: A = N, B = 2N , C = 2P(N) , D = [0, 1), E = ∅, F = Z × Z, G = {x ∈ N|x 2 + x < 2}, H = { 2 n 3 k |n, k ∈ N}, I = R \ Q, J = R. Consider the relation ∼ on S given...
The function f(x, y) is defined by f(x, y) = 5x^3 * cos(y^3). You will compute...
The function f(x, y) is defined by f(x, y) = 5x^3 * cos(y^3). You will compute the volume of the 3D body below z = f(x, y) and above the x, y-plane, when x and y are bounded by the region defined between y = 2 and y =1/4 * x^2. (a) First explain which integration order is the preferred one in this case and explain why. (b) Then compute the volume.