(a) Calculate lim f(x) if it exists. If it does not exist write “DNE”. x→4 lim f(x) x →4 - (b) Find the value of k so that f is continuous at x = 4. k =

Q: Find a 1-1 function f from J onto S where Sis the set of all odd integers.

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Q: The following functions all have {1, 2, 3, 4, 5} as both their domain and codomain. For each,…

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Q: Given f: R → R where f(x) = -3x² +7 Is it a function or not? If function, identify whether it is…

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Q: Question 3 Let f: A → B and g: BC be functions. If gf is one-to-one, prove that f is one-to-one.

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Q: Suppose  f:A->B  and g:B->C are one- to -one functions show that   f of A->C : is One-to-one

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Q: A function f : Z Z is defined by f(n) = 3n + 1. Let E be the set of even %3D integers. Determine the…

A: When a function is linear, it is one-one and onto function. We know that a bijective function is…

Q: Let f: XY and A,BCX. Give an example of a function f and sets A and B that f[A\B] #f[A]\f[B]

A: Take any constant function and subsets A and B such that they overlap.

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

A: Given functions:

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: Let g : B → C and h : B → C be functions. Suppose that go f = hof for every function f: A → B. Prove…

A: We have to prove that g(x) = h(x) for all x belongs to B.

Q: Prove or provide a counterexample to the following statement: if f : A → B and g : B → C are…

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Q: : Let f [a, b] → R be a continuous and one-to-one function, where a < b are real numbers. Use the…

A: Introduction: There must be at least one "c" such that c∈(a,b) (or a&lt;c&lt;b) and f(c) = L. if…

Q: Let f(x) = x and g(x) = x-8. Determine the composite functionfog and its domain. %3D (fo g)(x) =…

A: given that fx=x and gx=x3-8determine the composite function fog and its domain

Q: - Determine whether the following function is analytic f (2) = z Re z + z Im z + z.

A: The objective is to determine whether the given function is analytic or not. Given: fz=zRez+z¯Imz+z¯

Q: If ƒ : R → R and g : R → R are both one-to-one, is f + g one-to-one? If f and g are both onto, is f…

A: As per the guideline I’m supposed to solve only first question from the given questions. And the…

Q: If f : X → Y and g: Y→ Z are functions such that g of is one-to-one, then f is one-to-one.

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Q: Let f be a function defined on an interval I. All we know about f is that there is a constant K> 0…

A: Concept:

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: Either prove the following statement or disprove it by giving a counterexample: Let f : A → B and g:…

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

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Q: f is also constant

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Q: Determine whether Rolle's Theorem applies to the following functions on the given interval. If so,…

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Q: Given f: R → R where f(x) = x³ Is it a function or not? If function, identify whether it is…

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Q: Suppose f: Q+ → Z+ is defined by = mn for all positive integers m and n. Indicate whether f is a…

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Q: Prove the following properties for even and odd functions. a) (Even)(Even)=Even

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Q: g(x) = x²mx, -2, mx+b, if x 1.

A: We can solve this as follows:

Q: Consider the function f(n) = floor(n/2) from Z to Z. a. Is this function one-to-one? Is this…

A: Now, we have fn=floorn2 Part a A function is said to be a one-one function if no two elements from…

Q: Prove the following statements: (a) If f : A → B and g : B → C are one-to-one functions, then go f:…

A: We prove that if f : A → B and g : B → C are one-to-one functions, then go f : A → C is one-to-one.…