Question

Determine which of the following functions are injective, surjective, bijective (bijectivejust means both injective and surjective)....

Determine which of the following functions are injective, surjective, bijective (bijectivejust means both injective and surjective).

(a)f:Z−→Z, f(n) =n2.

(d)f:R−→R, f(x) = 3x+ 1.

(e)f:Z−→Z, f(x) = 3x+ 1.

(g)f:Z−→Zdefined byf(x) = x^2 if x is even and (x −1)/2 if x is odd.

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
2) Characterize the following functions in terms of whether they are injective, surjective, and/or bijective. If...
2) Characterize the following functions in terms of whether they are injective, surjective, and/or bijective. If possible, find their inverses. a. ?:ℝ+ → ℝ+ with ?(?) = ?3 b. ?:ℤ+ → ℤ+ with ?(?) = ?3 c. ?:? → ? with ? being the set of calendar dates and ?(?) being the day numbered ? in the next month that has that day. For instance, if ? is January 22, 1981 and ? is March 31, 1993, ?(?) is February...
Part II True or false: a. A surjective function defined in a finite set X over...
Part II True or false: a. A surjective function defined in a finite set X over the same set X is also BIJECTIVE. b. All surjective functions are also injective functions c. The relation R = {(a, a), (e, e), (i, i), (o, o), (u, u)} is a function of V in V if V = {a, e, i, o, u}. d. The relation in which each student is assigned their age is a function. e. A bijective function defined...
Let X, Y and Z be sets. Let f : X → Y and g :...
Let X, Y and Z be sets. Let f : X → Y and g : Y → Z functions. (a) (3 Pts.) Show that if g ◦ f is an injective function, then f is an injective function. (b) (2 Pts.) Find examples of sets X, Y and Z and functions f : X → Y and g : Y → Z such that g ◦ f is injective but g is not injective. (c) (3 Pts.) Show that...
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 :...
For each of the following pairs of functions f and g (both of which map the...
For each of the following pairs of functions f and g (both of which map the naturals N to the reals R), state whether f is O(g), Ω(g), Θ(g) or “none of the above.” Prove your answer is correct. 1. f(x) = 2 √ log n and g(x) = √ n. 2. f(x) = cos(x) and g(x) = tan(x), where x is in degrees. 3. f(x) = log(x!) and g(x) = x log x.
Consider the cubic function f: x^3 -10x^2 - 123x + 432 a) Sketch the graph of...
Consider the cubic function f: x^3 -10x^2 - 123x + 432 a) Sketch the graph of f. b) Identify the domain and co-domain in which f is NOT Injective and NOT surjective. Briefly explain c) Identify the domain and co-domain in which f is Injective but NOT Surjective. Briefly explain d) Identify the domain and co-domain in which f is Surjective but NOT Injective. Briefly explain e). Identify the domain and co-domain in which f is Bijective. Explain briefly
Exercise 9. In the questions below you can describe the relations/functions either by drawing a diagram,...
Exercise 9. In the questions below you can describe the relations/functions either by drawing a diagram, by a formula, or by listing the ordered pairs. Explain your solutions. (i) Give an example of two sets A and B and a relation R from A to B which is not a function. (ii) [hard] Find a set A, |A| = 4 and define a bijective function between A and P(A)? If such a set doesn’t exist give a reason. Exercise 11....
For each of the following pairs of functions f and g (both of which map the...
For each of the following pairs of functions f and g (both of which map the naturals N to the reals R), show that f is neither O(g) nor Ω(g). Prove your answer is correct. 1. f(x) = cos(x) and g(x) = tan(x), where x is in degrees.
Determine whether each of the following functions is an injection, a surjection, both, or neither: (a)...
Determine whether each of the following functions is an injection, a surjection, both, or neither: (a) f(n) = n^3 , where f : Z → Z (b) f(n) = n − 1, where f : Z → Z (c) f(n) = n^2 + 1, where f : Z → Z
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT