5) Which of the following is true? If f(x) = In x, then A) both the domain and the range of f are all positive real numbers. B) both the domain and the range of f are all real numbers. C) the domain of f is all real numbers except zero and the range is all real numbers. D) the domain of f is all real numbers and the range is all positive real numbers. E) the domain of f is all positive real numbers and the range is all real numbers.

Q: There is a real number whose product with every real number equals zero. a. Some has the property…

A: Note: As per company guidelines we are supposed to solve 1 question. So, kindly repost other…

Q: Determine the set of all real numbers x such that x-9 exists. x2-9

A: x-9x2-9

Q: If x, y and z are three real numbers such that x+ y+ z= 4 and x + y + z = 6, then show that each of…

A: Introduction :

Q: Prove or disprove: The inequality 1/(2^x) ≤ 1/(x + 1) is true for all positive real numbers x

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Q: Prove the following theorem using direct proof 1. For every pair of positive real numbers x and y,…

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Q: Assume that a and b are real numbers such that a <b. Prove that the interval (a,b) is an open set.…

A: Given that a and b are real numbers and a&lt;b. Prove that (a,b) is an open set

Q: Let x and be real numbers. Prove that a2 = y? if and only if a = y or æ = -y.

A: Let                x2=y2⇒x2-y2=0⇒(x-y)(x+y)=0⇒x=y  or  x=-y So, x2=y2 only if x=y  or  x=-y.

Q: Prove that if x is a real number, then ⌊2x⌋ = ⌊x⌋ + ⌊x + 1/2 ⌋.

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Q: Show that if x+yi=(a+bi)- is true, then x-yi=(a-bi)-is all real numbers). true (x, y, a, and b are

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Q: Describe the set of real numbers satisfying Ix - 31 = Ix - 21 + 1 as a half-infinite interval.

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Q: Prove for all rational number x and y and all irrational number r. If (r+x)/(r+y) is rational then…

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Q: Let x and y be two real numbers such that x + y is rational. Prove by contrapositive that if x is…

A: Introduction: Rational and irrational numbers are two very important divisions of real number…

Q: Let the domain of x be the set of real numbers. Then 3x, (x³ = x) is a true statement

A: Let x = 1  So we have x3 = 13 = 1

Q: 7. If the domain of f is all real numbers in the interval [0, 7] and the domain of g is all real…

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Q: The domain of g(x) = 3 consists of all real x - 2 numbers except 2, represented in interval notation…

A: Given :          g(x) = 3x-2 To determine :              The domain of g(x) interval notation

Q: Does the Nearest Point Theorem in R imply that there is a strictly positive real number nearest…

A: The statement of the Nearest Point Theorem is as follows: "Let A be a non-empty closed convex set in…

Q: Prove that if æ is a real number, then [2a] = [x] +

A: If x is a real number then  to prove- 2x=x+x+12 Greatest integer function is denoted by [x] for any…

Q: Let the domain of x be the set of negative real numbers. Then Vx, (1+ x² > 0) is a true statement a…

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Q: Prove: Use a contradiction argument to show that √ is not a rational number.

A:

Q: 1. prove that if x is real number then ,[2x] =[x] +[x +1/2] when [x] denote the greatest integer…

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Q: Use proof by contradiction to show that there is no positive real number x such that (x-2)/x ≥…

A: In an inequality, if a positive number is multiplied then there is no change of sign of inequality.…

Q: Show that if f1(x) isΘ(g1(x)), f2(x) isΘ(g2(x)), and f2(x) ≠ 0 and g2(x) ≠ 0 for all real numbers x…

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Q: Find a set of four integers such that their order and the order of their absolute values are the…

A: We have to find a set of four integers such that their order and the the order of their absolute…

Q: Let c, a, B be nonzero real numbers such thatc + B. Find a given that

A: This question is taken from the series and sequences in which we have to find the value of the alpha…

Q: If the domain of f is all real numbers in the interval [ 0, 7],and the domain of g is all real…

A: We know that if the domain of function f is a, b and the domain of function g is c, d then the…

Q: Show that for any real numbers X and y. one of the following two case can happen: Either [x+Y = [×]…

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Q: Let x and y be real numbers. Disprove: If |x| < |y| then |x+1|< |y+1]. Let x, y, and z be real…

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Q: Let x be an element of the real numbers. Prove |x| is greater-than or equal to 0. State any theorems…

A: For any real number x , the absolute or modulus of x is denoted byx and is defined as x=x , if…

Q: The set of all real numbers x for which x24x+2+x>0 is

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Q: Suppose x is a real number. Prove that if x 2, then there is a real number y such that x = (2y + 1)/…

A: Domain of a Function The domain of a function explains what values the independent variable, X, can…

Q: Show that : [x+y] > [x] + [Y] for any real numbers x and y

A: Introduction: The greatest integer function is a significant number theoretic function. Every real…

Q: Prove that x (x-2) is always a negative real number if x 1-Ai for some real number A.

A: The given number is  x(x - 2) x = 1 - Ai

Q: If x and y are real numbers and x>1, prove that there exists a positive integer n such that x" > y

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Q: What is the set R of all real numbers?

A: Real numbers are the numbers which include both rational and irrational numbers. A real number is a…

Q: The domain of g(x) =3/(x - 2)consists of all real numbers except 2,represented in interval notation…

A: To Determine: The domain of g(x) interval notation as (- ∞, 2) ∪________. Given: we have a function…

Q: (1) Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute…

A:

Q: Express the set of real numbers between but not including 2 and 7 as follows. (a) In set-builder…

A: Set: In set builder notation the real number between 2 and 7 but not including both the numbers, Let…

Q: Prove that the product xy of two real numbers x and y is nonnegative if and only if the absolute…

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Q: Prove that if x is real number then L2xd =LxJe bx+!]

A: We will prove the expression by two  steps taking real number x in two form.

Q: Find the maximum value of f(x)=x^3-3x on the set of all real numbers x satisfying x^4+36< (less then…

A: Given: The function fx=x3-3x To find: The maximum value of given function on the set of all real…

Q: Let x, Y be positive real numbers. If x2 – y² =1, then x or y (or both) is not an integer.

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Q: Let x be a real number. Prove by contrapositive that if x' + 7x = 90, then x < 4.

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Q: Prove or Disprove. for any real numbers x and y, |x+y| = |x| + |y|

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Q: The Archimedean Property says that the set of real numbers have no upper bound. True or False

A: Given a statement , we have to check whether it is true or not. As we know the property of…

Q: . Prove that |x|+ |x + ;] = |2x| for any real number .

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Q: Let x be a real number. Show that 1 [3x] = [x] + | x + - 3 3 ++1+

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Q: Use a direct proof to show that if x is a real number such that (x – 1)? = 0, then x³ –1 = 0.

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Q: 1 1 2 x y x+y || +

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.