Which of the following function f: R X R → R is not onto?   1 2x - 3   2 3x3 - x   3 x2-2x   4 f(x) = x2- 5x + 5

Q: Give the domain of the function. z = 4x – 5y O {(x, y): x and y are real and 4x – 5y = 0} O {(x, y):…

A:

Q: Determine whether or not the function f : Z × (Z − {0}) → Z is onto, if f((m, n)) = ⌊mn ⌋.

A:

Q: b. In Z6(x], let f = 2 + x + 4x² + 3x³ and g = 4 + 3x+ 5x² + 3x³. Compute f + g and f.g and their…

A: In the finite field we only use the coefficients from that field . The degree of polynomial is not…

Q: 1. Let f : Z6 → Z6 be such that f(7) = x2 + 3. (a) Is f a well defined function? (b) Is f…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Suppose f(x) : a.x+6 for real numbers a, b, c with both a and c not zero. сх—а (a) Find the domain…

A:

Q: Are the following functions 1-1, onto, both, or neither. f: R-R. f(x) = x13 h: Z- Z. h(x) = x g:…

A:

Q: Let z be the set of integers and f:Z→Z be de fined as f(x) =-7x+2. Then the inverse function of f *…

A: Does not exists because f is not onto.

Q: Determine the kernel and range of each of thefollowing linear operators on R3: L (x) = (x1, x1, x1)T

A: It is given that,

Q: 4. Show that a sublinear functional p satisfies p(0) = 0 and p(-x) ≥-p(x).

A:

Q: 15. Determine whether the function f: Z x Z Z is onto if a) f(m, n) =m+n. b) f(m, n) = m² + n². c)…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 2. Consider the following four functions from R into R, determine if onto or 1-1 function. Support…

A: To find out which of the following function is one-one,  onto .

Q: Which of the following function f: Z x Z Z is not onto? 2020 a. f(a, b) = a b. f(a, b) = lbl c. f(a,…

A:

Q: b) A function g:Z→Z is defined by the rule g(m, n) = m + n Determine whether it is onto or not...

A: A function f:A→B is said to be onto or surjective if for all element b∈B there is an element a∈A…

Q: Prove that if f : [-1,1] → R is measurable, then |f| is also measurable.

A:

Q: 1. Let f : Z6 → Z6 be such that f(a) = x2 + 3. (a) Is f a well defined function? (b) Is f…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Let A = R - {O} and B = R. For the givenf: A----- B, decide whether f is onto and whether it is…

A: f(x) = xx2+1Let x,y be any two elements of ASuch that, x is greater than 0 and y is greater than…

Q: then L is a linear operator. Let L(x). R R be a mapping such that L( X2 Select one: O True O False

A: We will check whether the given statement is true or false.

Q: Let Z be the set of integers and f:Z Z be defined as f(x)=-2x-3. Then the inverse function of exists…

A:

Q: Prove directly from the definition that if X and Y are independent and f and g are measurable…

A: Solution: Given X and Y are independent and f and g are measurable function then we have to prove…

Q: 5. Determine whether the function f : Z × Z →Z is onto if a) f (m, n) = m² + n² b)f (m, n) = m³

A: See the solution.

Q: Exercise 2.12. Determine whether or not the given functions f:Z Z are one-to-one or onto (or neither…

A: The solution of given functions is given as follows :

Q: 1. Consider the functions f : A → B and g : B → C. (a) If f and g are both surjective, show that so…

A:

Q: For a bijective function f:(X,r1)→ (Y,12), one of the following statements is true: O f is open if…

A:

Q: Prove that a function f: AB is surjective if and only if it has the following property: for every…

A:

Q: 5. Let 2x g(x) = ,0 3 find (go g)(x)

A: Given function, We know that ( g o g )(x) = g(g(x) ).

Q: 1. Determine whether each of these functions is a bijection from R to R. a) f (x) = 5x + 10 %3D B) f…

A: A function f:A→B is bijective if it is both injective and surjective. A function is injective if…

Q: Determine the kernel and range of each of thefollowing linear operators on R3: L (x) = (x1, x2, 0)T

A:

Q: Let s(x) and c(x) be two functions satisfying s′(x) = c(x) and c′(x) = −s(x) for all x. If s(0) = 0…

A: Given, s′(x) = c(x) and c′(x) = −s(x) for all x. If s(0) = 0 and c(0) = 1, To prove:     [s(x)]2 +…

Q: A function g: Z → Z is defined by the rule g(m,n)=m+n Determine whether it is onto or not...

A: Onto functions: A function f: A→B is said to be an onto function if range of function is equal to…

Q: Show that the function f: N→N, defined by x + 1, if x is odd f(x) = x – 1, if x is even is one-one…

A:

Q: a. The function f : Z → Z, f(x) = 2x is onto. (A) True (В) False b. The function f : Z → Z, f(x) =…

A:

Q: A function f is ________ when there exists a positive real number c such that f (t + c) = f(t)for…

A: We know that for a functionft, if there exist a positive real number c such that ft+c=ft, for all t…

Q: 6. Prove that there does not exist a multiplicative function f such that f(30) = 0, f(105) = 1, and…

A: We have to prove the given statement.

Q: For each of the functions below, indicate whether the function is onto, one-to-one, neither or both.…

A:

Q: Which of the following is indeterminate at x = 1? x2 +1 х2 — 1 x² – 1 x² +1 х — 1" x +2 Vx +3 – 2'…

A:

Q: Consider the following bijections on R: f (x) = - g(x) = x – 7 Then (f o g)¯'(x) =

A: Given, fx=-x,gx=x-7 Find the value of f∘g-1x.

Q: Suppose f : N→N and g :N→N , function f is not onto but f+g is onto function  does g onto function…

A: g is not necessary to be onto. See the attachment

Q: Suppose  there exist transposition f_i , 1<=I<=t  such that

A:

Q: 3. а) Prove by induction that 1 P(n):2+6+12+20+...+n(2n+2) =n(n+1)(n+ 2) Vn21 1 3 Let f:R→(-1,1) be…

A: For part a, principle of mathematical induction is used. For part b, function is defined when imagee…

Q: 3. а) Prove by induction that 1 P(n):2+6+12+20+...+n(2n+2) = n(n+1)(n+2) Vn21 2 1 3 Let f:R→(-1,1)…

A: For a, principle of mathematical induction is used. For b, function is not well defined as images of…

Q: Which of the following function f: Z XZ → Z is not onto? f(a, b) = a O f(a, b) = |b| f(a, b) = a - b…

A:

Q: I c exists in (0, 1) such that f(c) (1)- f(0) 1-0

A:

Q: (b) Let f(x) and g(x) = x² + 1. x + 2' ii. Determine if f and g are one to one or onto. iii.…

A:

Q: ) Let f: A-B be a function which is not surjective and g : B C which is bijective. Prove that g of:…

A: See full proof below

Q: Let x ∈ R. Prove that if x3 − x > 0 then x > −1.

A:

Q: Letf(x) = (x - 1)(x - 2)(x - 3) Prove that there is more than one 'c' in (1, 3) such that f' (c) =…

A: We have to find the value of c

Q: Prove that (a) IP{x) = (21 – 1)xP,-1(x) – (I – 1)P;- 2(x), (b) xP(x) – P; -1(x) = IP{{x), (c) P{(x)…

A: Disclaimer:- Since you have posted a question with multiple sub-parts, we will solve first three sub…

Q: There exists a function f such that f(-1) = –2, f(3) = 2, and f'(x) > 1 for all z. True O False

A:

Q: Suppose f : N → N and g : N → N are functions such that f is not onto but f + g is onto. May we…

A: Given: Two functions f : N → N and g : N → N are functions such that f is not onto but f + g is…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.