(a) Someone has claimed that since 14 is itself a multiple of 7, then there are more multiples of 7 than there are of 14. Show this is false by establishing 7Z - 14Z. (Do this formally, by establishing the appropriate function.)

Q: Prove that the function given by f(x) =x3-3x2+3x-100 is increasing in R

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Q: 2. If p and q are positive integers, f is a function defined for positive numbers and attains only…

A: Introduction :

Q: If f1(x) and f2(x) are functions from the set of positive integers to the set of positive real…

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Q: -2 is a critical number of the function f(x) = V2x - x². Select one: True O False

A: We can solve this as follows:

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A: The denominator can not be equal to 0  Because any constant divided by 0 is undefined

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Q: 7. If f(x) = mx²-x+2 and g(x) = 3x² +nx-4, and the points (-2, -14) and (1, -11) are on the combined…

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Q: Consider the following piecewise function where c is a constant real number. Зx2 + 5с х 2 3x2 + 5c x…

A: For limit to be existing both left side limit and right side limit should be equal

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A: You have asked two different questions. As per the company guidelines we are supposed to solve first…

Q: In this problem you will use Rolle's theorem to determine whether it is possible for the function…

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Q: 59. Which statement about the function f(x) = 3x2 – 14x - 5 is true? A The expression 3x2 – 14x - 5…

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Q: . Show that the function f: R→ R defined as f(x) = 13x − 15 is one-to-one.

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Q: x -4x +5 - Prove that: f' x x-2

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: Pierre de Fermat (1601–1665) conjectured that the function f(x) = 2(2x) + 1 for x = 1, 2, 3, c,…

A: To determine the prime numbers

Q: (a) Prove or disprove: f: Z3 → Z5, [x]3 → [x³]5 is well defined. (b) Prove or disprove: f: Z10 →…

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Q: 2 is the graph of f(x) = -2/3 x – 3. -6 -5 -4 -3 -2 -10 1 2 3456 -2 -3 -4 -5 O False True

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Q: 8. Show that the function f : N → Q defined by f(n) n- is one to one. n+1

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Q: Find the function f if it is known that f prime of x= 3x^2 +6x-7 and f(-1)=10.

A: Given: f'x = 3x2 + 6x - 7 and f-1 = 10 To find: fx

Q: Show that f 1 (3) does not exist.

A: Given : To show f'(3) doesnot exists

Q: 3. For f (x) = 2x³ + 4x² + 3x – 7, prove that there exist a number k such that f(k) = 20.

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Q: 5.5 (a) Determine the roots of f(x) = -12 – 21x + 18x2 – 2.75x3 graphically. In addition, determine…

A: Given: f(x)=-12-21x+18x2-2.75x3 To determine: Root of given function by a) graphing method. b)…

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Q: 2- Let g(x) = x5 - 8.6x* + 38.782x3 - 17.25x² - 4.5927x + 10.5 then the value of g(0.25 x 101) =…

A: The objective is to state whether the statement is true or false. For the polynomial…

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Q: What is the smallest integer a where f(x)=2x is always greater than g(x)=x2 for all x>a?

A: Given  : f(x) = 2x is always greater than g(x)=x2 for all x &gt; a  Implise that :  2x &gt; x2

Q: (a) Is it possible that f(1) = 9 and f(2) = 9? Yes. No. A function assigns each value of x in its…

A: To determine whether yes or no.

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Q: 5.5 (a) Determine the roots of f(x)= -12 – 21x+ 18x? – 2.75x3 graphically. In addition, determine…

A: Solution 5.5: f(x)=-2.75x3+18x2-21x-12 The graph of the function between xl=-1 and xu=0 Since the…

Q: Suppose that the function g is defined, for all real numbers, as fo -4 if x < -2 g(x) = (x+1)²…

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Q: 5. Consider the function Ax) =- 2x + 3x - 8. Determine k + 4). 4).[ 3A]

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: 5.5 (a) Determine the roots of f(x)=-12 – 21x + 18x2 – 2.75x³ graphically. In addition, determine…

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Q: 1. Suppose that f2(x) is a measurable function. Is it true that f(r) is measurable? Prove, or give a…

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Q: 5. Consider the function Ax) = - 2x + 3x - 8. Determine * + 4).[ 3A]

A: 5. Given function   f(x)=-2x2+3x-8 We need to find f(k+4)

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Q: Suppose If(x)-7| 0 such that |f(x) – 7| < 0.1 whenever 0< |x - 1 < 8. The values of 8 are 0<8sN.…

A: Given that fx-7&lt;0.7 whenever 0&lt;x&lt;7.

Q: Prove that the product of an odd function and an even function is odd.

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Q: -2 is a critical number of the function f(x) = /2x - x2, Select one: O True O False

A: The given function is  f(x)=sqrt(2x-x2)

Q: For f(x)=2x3+4x2+3x-7, prove that there exist a number k such that f(k)=20.

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Q: Suppose that the functionh is defined, for all real number 1 2 x++5 if x -2 h (x) = < %3D -3 if x…

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Q: a. Show that f has a removable discontinuity at x = 3. x² - 7x + 12 f(x)= x - 3 x = 3

A: Removable discontinuity

Q: Which among the following is an even function     x2 + 1     (x + 1)2     x2 + x     (x +…

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Q: 7. Please refer to the following functions: p(x) = x2 + 2x - 15 x +1 q(x) : x-3 r(x) = v7-x Which of…

A: Please refer to the image below