7. Determine whether each of these functions is one-to-one or onto. (a) f:Z + Z, f(n)...
For each of the following functions, state whether or not the function is one-to-one, onto, both, or neither: 1) f : Z → Z defined by f(x)=2x + 1; 2) f : R → R defined by f(x)=2x + 1;
For each of the following functions, determine whether or not they are (i) one-to-one and i) onto. Justify your answers (a) f : R-{0} → R and f(x) = 3r-1/x (b) g : R _ {1} → R and g(x) = x + 1/(x-1) (c) l : S → Znon-reg and l(s) = number of 1's in s, for all strings s E S, where s is the set of all strings of O's and 1's. (d) 1 : S...
Question 1 (10 points) Which of the following functions is not an onto function? f: R → R, where f(x) = 2x + 7 f: R – R, where f(x) = 6x - 1 Of: Z – Z, where f(n) = n + 3 f: Z - Z, where f(n) = 3n + 1
please.show work and answer full.question. this js discrete math. 1. Determine whether each of the functions is one-to-one and/or onto. a. f:R - R, f(x) = 19(x) = log2(x) one-to-one onto onto one-to-one b. f:N NX N, f(x) = (x,x) onto one-to-one c. f:R+ (-1,1), f(x) = cos(x) one-to-one onto d. 8:[2,3) –> (0, +), f(x) = ***
(g(n)), g(n) is (f(n)), or both. 1. For each of the following pairs of functions determine if f(n) is f(n) = (na – n)/2, g(n) = 3n · f(n) = n log n, g(n) = n/n/2
12. From the given functions from Z × Z to Z, identify the onto functions. (Check all that apply.) From the given functions from Z x Z to Z, identify the onto functions. (Check all that apply) Check All That Apply Am, n) 2m-n Am, n)= m2 - n2 Am, n) m+n+1 Am, n)= m - |n! Am, n) m2-4 From the given functions from Z x Z to Z, identify the onto functions. (Check all that apply) Check All...
Determine which of the following functions are injective, surjective, bijective (bijectivejust means both injective and surjective). And Find a left inverse for f or explain why none exists.Find a right inverse for f or explain why none exists. (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.
a. A function f: A B is called injective or one-to-one if whenever f (x) f(u) for some z, y A then y. Which of the following functions are injective? In r-y. That is Vr,y E A f()-f(u) each case explain why or why not i. f:Z Z given by f(z) 3 7 ii. f which maps a QUT student number to the last name of the student with that student number. b. Suppose that we have some finite set...
3. Determine algebraically whether each of the following functions is one-to-one. Show your work! (a) f(x) = 4x2 4x (b) g(x) 3x + 2 2x – 1
k Determine whether the rule describe a function with the given domain and target. You must provide a specific counterexample if you determine it is not a function. (Note that the symbol squareroot refers to the principal or positive square squreroot .) f:R rightarrow R where f(x) = sqaurerootx f:Z rightarrow where f(n) = squaretrootn^2 + 1 For c, d and e below, consider the function: f: {0,1}^n rightarrowZ (i.e., f maps elements from the set of all bit strings...