Question

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

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
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.
Determine which of the following functions are one to one and explain your reasoning. 1. f(x)=...
Determine which of the following functions are one to one and explain your reasoning. 1. f(x)= x2-3x-10 2. g(x)= -2x3+1
Determine the intervals on which the following functions are increasing and decreasing. a) f(x) = 12...
Determine the intervals on which the following functions are increasing and decreasing. a) f(x) = 12 + x - x^2 b) g(x) = 2x^5 - (15x^4/4) + (5x^3/3)
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...
1. Differentiate the following functions. Do not simplify. (a) f(x) = x^7 tan(x) (b) g(x) =...
1. Differentiate the following functions. Do not simplify. (a) f(x) = x^7 tan(x) (b) g(x) = sin(x) / 5x + ex (c) h(x) = (x^4 + 3x^2 - 6)^5 (d) i(x) = 4e^sin(9x) (e) j(x) = ln(x) / x5 (f) k(x) = ln(cot(x)) (g) L(x) = 4 csc^-1 (x2) (h) m(x) = sin(x) / cosh(x) (i) n(x) = 2 tanh^-1 (x4 + 1)
Suppose the following functions have inverses on their domains. (1) f(x) = 4ecos(4x). Find and explicit...
Suppose the following functions have inverses on their domains. (1) f(x) = 4ecos(4x). Find and explicit formula for f-1(y). (2) g(x) = log3(tan(x)). Find an explicit formula for g-1(y).
determine whether each of the following functions are one-to-one by using the horizontal line test. (a)...
determine whether each of the following functions are one-to-one by using the horizontal line test. (a) f(x) = x2 + 5 Yes, it is one-to-one. No, it is not one-to-one.      (b) g(x) = 3x3 + 2 Yes, it is one-to-one.No, it is not one-to-one.      (c) h(x) = |x - 2| Yes, it is one-to-one.No, it is not one-to-one.    
3) If A =     3   1     and   B =    1    7                   0 -2  &
3) If A =     3   1     and   B =    1    7                   0 -2                     5    -1 Find a)      BA            b) determinant B         c) Adjoint A                d) A-1                     4) Using matrix method solve the following simultaneous equations                           5x – 3y = 1                         2x – 2y = -2    5) Given that f(x) = 6x - 5 g(x) = 3x + 4 and h(x) = 4x – 6                                                                                          2     Find:- i)...
Determine whether the given set ?S is a subspace of the vector space ?V. A. ?=?2V=P2,...
Determine whether the given set ?S is a subspace of the vector space ?V. A. ?=?2V=P2, and ?S is the subset of ?2P2 consisting of all polynomials of the form ?(?)=?2+?.p(x)=x2+c. B. ?=?5(?)V=C5(I), and ?S is the subset of ?V consisting of those functions satisfying the differential equation ?(5)=0.y(5)=0. C. ?V is the vector space of all real-valued functions defined on the interval [?,?][a,b], and ?S is the subset of ?V consisting of those functions satisfying ?(?)=?(?).f(a)=f(b). D. ?=?3(?)V=C3(I), and...
1. Create a script named AnonIntegrals.m. Within it, define each of the following functions as anonymous...
1. Create a script named AnonIntegrals.m. Within it, define each of the following functions as anonymous functions and use the integral command to compute its definite integral over the domain given. Display the integral calculation to the command window. (a) p(x) = 4x 2 − 1, x ∈ [0, 1] (b) q(x) = sin(x), x ∈ [0, π] (c) r(x) = cos(x), x ∈ [−π/2, π/2] (d) s(x) = log(x), x ∈ [0, 1] (e) t(x) = 1 x ,...