If for each element y in Set B there exists an element x in Set A such that f(x) = y, then the function 'f'is called .... Select one: a. One to one function b. Constant function c. Onto function

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Q: Suppose that the functions g and h are defined as follows.

A: We have given two functions : g(x)=4x,x≠0 h(x)=x2-8 We have to find the composition functions g.gx…

Q: Suppose h is a function such that h(3) = - 2, h'(3) = 2, h'"(3) = 3, h(5) = 5, h'(5) = 7, h''(5) =…

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Q: Given the function f:{1,2,3} → N defined by f = {(1,3), (2,5), (3,1)} Is f1-1 Is f onto What is the…

A: We know that one to one functions are functions that return a unique range for each element in their…

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

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Q: function is defined as c*x^1 from 1 to 5 and 0 otherwise. What is c?

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Q: For a function g(x), if there exists x E [a,b] such that g'(x)> 1, then we conclude that g(x) has…

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Q: Eliminate the arbitrary function in the following and hence obtain the corresponding PDE

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Q: If f(a) > f(x) in an open interval containing a, x + a, then the function value f(a) is a relative .…

A: Given: If f(a)>f(x) in an open interval containing a, x≠a, then the function value f(a) is a…

Q: If f(a) > f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a…

A: Definition:

Q: For any k > 0 E Z, show that there is a function f : Z* → Z which is both one-to-one and onto. (Here…

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Q: Let fand q be two boundes measurable Functionset E. prove thet if fu)-g(x) a.e. on E theh

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Q: Suppose h is a function such that h(3) = -2, h'(3) = 2, h"(3) = 4, h(5) = 6, h'(5) = 7, h"(5) = 13,…

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Q: Suppose that g is an even function of x and h is an odd function of x. Show that if g(x) + h(x) = 0…

A: Consider that g(x) is the even function. Then, g(-x)=g(x) for all the value of x. Consider that h(x)…

Q: 6. Consider these functions from the set of students in a discrete mathematics class. Under what…

A: (a) The students from the set of student if it is assigned to his/ her mobile number is one to one…

Q: ctions, determine its domain, codomain, and range.    f: Z × Z → Z, f(m, n) = 3m

A: Introduction: The Domain refers to what can be put into a function. The Codomain is what may or may…

Q: For a function g(x), if there exists x E[a,b] such that g'(x)> 1, then we conclude that g(x) has not…

A: For a function g(x), if there exists x∈[a,b] such that g'(x)> 1, then we conclude that g(x) has…

Q: A on S is a function from S×S into S.

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Q: Let f(x) = xe¬** be defined on [1, 00) and let an f(n) for positive integers n.

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Q: Suppose that the function h is defined, for all real numbers, as follows.

A: Given, h(x)=12x-1                  if x≤-2-x+12+2        if -2<x≤1-14x-2              if x > 1

Q: The smallest number c for which a function f is periodic is the ________ of f.

A: Given The smallest number c for which a function f is periodic is the ________ of f.

Q: If F is a function from A to B and x is an element of A, then F(x) is ________.

A: It is given that F is the function from A to B.It is known that if A and B are sets and F is a…

Q: if g(x) is an odd function defined for all values of x,what can you sat about g(0)

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Q: Define H(x) as a piecewise defined function and evaluate H(1), H(2), H(3), H(0) and H(-2) given by,…

A: We have to solve the problem by just putting the value in the piecewise function.

Q: Suppose that f : A → B and g : B → C are both injective functions, prove that the function go f : A…

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Q: 18. Let f: Z →Z and g: Z→Z be defined as follows. In each case, compute (f ° g)(x) for arbitrary x E…

A: Given: f(x)=x+x and g(x)=x2,if x is even-x,if x is odd To find: f∘gx

Q: Suppose that the functions u and w are defined as follows. u (x) = x²+1 w (x) = /x+6

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Q: Let f(x) = { 3, 1< x < 2 0, 2 < a <5 and Let F(x) = { 3x, 1<x < 2 6, 2 <x < 5 Show that wether the…

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Q: Suppose f and g are functions with domain R. If both f and g are even but f+g is odd, then prove…

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Q: Determine whether each of the following statements is true or false, and explain why. A critical…

A: Given statement is "A critical number c is a number in the domain of a function ƒ for which ƒ′(c) =…

Q: Suppose that the functions u and w are defined as follows.

A: Given functionu(x)=x2+6w(x)=x+9we have to find(a) (uow (7)(b) (wou) (7)(a) (uow) (7)It mean u (w(7))…

Q: Suppose h is a function such that h(2) = -2, h'(2) = 2, h"(2) = 4, h(5) = 5, h'(5) = 7, h"(5) = 12,…

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Q: 4. a) Determine if the credit card number 4147180124197779 has a correct check digit. Is this a…

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

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Q: 4. Give an example of a function from N to N that is (a) one-to-one but not onto. (b) onto but not…

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Q: Consider these functions from the set of students in a discrete mathematics class. Under what…

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Q: For a function g(x), if there exists x E [a,b] such that g'(x) > 1, then we conclude that g(x) has…

A: Solution: Given, gx is a function and there exists x∈a,b such that g'x&gt;1. Then, gx has not a…

Q: Suppose that the function h is defined on the interval (-2.5, 1.5) as follows. -2 if -2.5<x<-1.5 -1…

A: We can answer all the three questions as below.

Q: Let f : S → T be a function, and let A and B be subsets of T. Prove or give a counterexample to the…

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Q: Let {f} is sequence of measurable functions Let there exists F = { x: limf, (x) E } 1-00 Show that…

A: see my solution

Q: Let S be the set of all odd integers, and define a function f: Z → S as follows: f(n) = 2n + 1 for…

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Q: Suppose h is a function such that h(1) = -2, h'(1) = 2, h"(1) = 3, h(2) = 6, h'(2) = 5, h"(2) = 13,…

A: Given: The second derivative is continuous everywhere.

Q: Define a function S : Z+ → Z+ as follows. For each positive integer n, let S(n) = the sum of the…

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Q: Let A be a nonempty set and let f : A → B be a function. Prove that f is one-to-one if and only if…

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Q: If f(a)&gt; f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a…

A: If f(a)&gt; f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a relative…

Q: 1. For each of the following, either give an example matching the description of the function or…

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Q: Let function f:Z Z be defined as follows; x– 1 x is odd f(x) = < (x² + 2 x is even The function f is…

A: Let, x=2 that is x is even. Then, fx=x2+2 So, f2=22+2=6f-2=-22+2=6 Therefore, f2=f-2 Then, the given…

Q: Let f be a function on an interval I and let ₁ and 2 be any two points in I. Then if f (x₁) > f (x₂)…

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Q: Fined the in veľseofthe function aned Verify y in verseby comfuting both ofthe comfstion

A: Here is the solution