Q2 Let C = {x : x3 E Z}. (a) Show that CnQ # 0. (le. show C contains a rational.) (b) Prove that CnR \ Q + 0. (le. show C contains an irrational.) (c) Prove C is countable. (d) Is R\C countable or uncountable? Justify your answer.

Q: Domain and hange. Find the domain and range of the function. 5x² + 4 for 0 4 x 42 L

A:

Q: Q2: Iff (z) is analytic at zo. (b) Give an example to show that the converse of (a) is not…

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Q: The set of zeros of f(x) = x³ + 4x² + 4x is (B) {0, -2} (C) {0, 2} (D) {2} (A){-2}

A: find the zeros of the function fx=x3+4x2+4x

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A:

Q: If f (x) = x2 + 2x + 1, find f (x +1). O a) f (x + 1) = x² + 2x + 2 O b) ƒ (x + 1) = x² + 4x + 3 O…

A: Given f(x) = x2 + 2x + 1

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A: Intermediate Value Theorem.

Q: find the nUmbers b such that the auerage due of f(x)2+6x-3x on the interval E LO,b) is equel to 3

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Q: E.X; Let T = {E₁ = (-∞,a): a = R}U{R,Ø} be a topology on R and let A = [2,3), B=(3,4), C = (1,5], D…

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Q: Let f(x) = 3+√6 +7x. a) Find f-¹(x). f-¹(x) = 1/7x^2-6/7x+3/7 Correct. Good Job! Preview ƒ−¹(x) =…

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Q: What is the domain of the rational function(x)=-3x²-16x +48 Oxe 31x*-4,-2.3.4) Oxe 31x*-4, 3, 4) O…

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Q: 1on to ove tha (X +Y)(X + Y) =X

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Q: find the general slühion with real values fn +y(H)=0

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Q: expression

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A: Given,

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Q: Let f(x) = x4 − 9x3 + 23x2 − 15x − 10. Find an integer n1 so that f(x) has a root between x = n1 and…

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Q: 5.) Evaluate f(-3) for f(x) = x³ +3x + 17

A: Given  f(x) =x3+3x+17

Q: Prove that f(x) = 5x? + 3x – 26 is 0(x²). %3D

A: Given: f(x) = 5x2 + 3x – 26  is  θ(x 2).

Q: Is Z²-1 2-√√2²+4 analytic in 12/2

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Q: What are the roots of the function f(x) = x³ + x² − 7x -3? O 3, 1+√2, 1-√2 O -3,-1+√2, 1-√2 O 1, 3,…

A: Solution :-

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Q: 3. Is the polynomial f(x) = 2x° + 30r – 150 € Q(r] reducible or irreducible over Q? In either case,…

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Q: Find all rational roots of f(x) = 3x3 − x2 + 15x− 5.

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Q: (x+1)(x-2)². On what interval (2) (x - 5) let g"(x) = is g Concave up? (Note: you are given g" but…

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Q: (7) If x < 0 then 1/x < 0. (8) If 0<x<y then 0 <1/y < 1/x

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Q: 5. Use the Intermediate Value Theorem to show that f(x) = 3x³ – 10x + 9 has a real zero between -3…

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Q: Let fx)-1+x+x² and h = 0. (5+1)-(5)-(1)? (a) Does O Yes No Well done! (b) Find f(x + h). (c) Does…

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