F and H are sets of real numbers defined as follows. F={y|y>1} H={y|y<8} Write FU H and F N H using interval notation. If the set is empty, write Ø.

Q: Let a and b be real numbers. Prove that | a b | = | a | | b | , b ≠ 0

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Q: express the set of numbers x satisfying the given condition as an interval.       I x+ 7 I &lt; 2

A: Given: x+7&lt;2 We know that solution of inequalityx+a&lt;b is given by -b&lt;x+a&lt;b

Q: F and H are sets of real numbers defined as follows. F={v|v<3} H= {v|v≤5) Write Fn Hand FUH using…

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Q: B and C are sets of real numbers defined as follows. B-x |x<2} c={x |x27) Write Bn Cand BUC using…

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Q: If f(x) = and g(x) = z+3 %3D I-1 H-2 The domain of fogis the set of all real numbers except z+1

A: For f(g(x)) to be defined first g(x) needs to be defined

Q: Let the universal set be the set R of all real numbers and let A={x eR|-2<x<2} and B = {xe IR|-3<x <…

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Q: F and H are sets of real numbers defined as follows. F={v|v< 4} H={v]vs6} Write FO H and FUHusing…

A: F and H are sets of real numbersF=v|v&lt;4H=v|v≤6

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x)=2x-6 s(x)=x-4…

A: Given: Now, (s-r)(x)=s(x)-r(x)           =(x-4)-(2x-6)           =-x+2 (s.r)(x)=s(x)r(x)…

Q: Suppose that the functions s and t are defined for all real numbers x as follows. s (x) = 2x? t (x)…

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Q: Suppose that the functions and s are defined for all real numbers x as follows. r r(x)=x-6 s(x) =…

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Q: E and F are sets of real numbers defined as follows. E= {x | x 2 1} F = {x | x < 6} Write En Fand E…

A: We can write the answer as below using the given data set.

Q: I are sets of real numbers defined as follows. = {x | x > 2} %3D n H and FUH using interval…

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Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) =x s(x) =4x…

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Q: D and E are sets of real numbers defined as follows. D={x|x24} E= {x | x< 5} Write DUE and DnE using…

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Q: Suppose that the functions r and s are defined for all real numbers x as follows.  r(x) = x-5 s(x)…

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Q: Find the supremum and infimum of the set x € R:x = +(-1)" ,n e N} + (-1)" ,n e N}

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Q: A and B are sets of real numbers defined as follows. A-(: |2> 2} B-(: |258} Write AnBand AUB using…

A: Solution:   Given that A &amp; B are sets of real numbers such thatA = z | z&gt;2B = z | z≤8

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r (x) = 4x- 3 s…

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Q: Suppose that the functions s and are defined for all real numbers x as follows. s(x) = 2x 1(x) =x…

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Q: The interval ___________ consists of all real numbers for which x ≤ a.

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Q: Suppose that the possible values of æ is the interval (-3, ). This means that: - x -3 -3 < x < 3

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: use interval notation to represent all values of x satisfying the given conditions. y=7x-23+2(x+7)…

A: Given, y=7x-23+2(x+7) and y is at most 0

Q: F and H are sets of real numbers defined as follows. F={v|v<4} H={v]v<6} Write Fn H and FUHusing…

A: F = v|v&lt;4H = v|v≤6F∩H = those element/numbers continued in both F and H

Q: For all real numbers x and y, [x]+ [y] = [x + y] – 1. For all real numbers x, [x –1] = [x] – 1. | -

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Q: The function f(x) = 5 for x<2 and f(x) = 4 for x 2 2 has domain of all the real numbers. True O…

A: The domain is the set of all possible x-values which will make the function "work", and will output…

Q: express the set of numbers x satisfying the given condition as an interval.          I 4x - 1 I ≤ 8

A: 4x-1≤8

Q: Suppose that the functions r and S are defined for all real numbers r as follows. r (x) = 4x-3 s (x)…

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Q: Show that the equality [r + y] = [2] + [y] is not valid for all real numbers r and y.

A: Consider the provided question, We first define ceiling function. The ceiling function maps x to the…

Q: F and H are sets of real numbers defined as follows. F={y|y21} H= {y |y>7} Write FUH and FnHusing…

A: A set is a well-defined collection of objects. The objects, which belong to the set, are called…

Q: C and D  are sets of real numbers defined as follows. C={y|yless than or equal to 4}   D={y|y…

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Q: Which of the following expressions is equivalent to for all positive real numbers x and y ?

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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: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) = 4x-6…

A: Calculate r-sx. r-sx=rx-sx               =4x-6-x-3               =4x-6-x+3               =3x-3

Q: A and B are sets of real numbers defined as follows. A = {z | z2 3} B = {z | z< 8} Write A N B and A…

A: Consider the provided information, A=z| z≥3B=z| z&lt;8 We can write as,…

Q: Use interval notation to represent all values of x satisfying the given conditions: y = 2x - 11 +…

A: It is given that,y = 2x - 11 + 3(x + 2) and y is at most 0. We have to use interval notation to…

Q: express the set of numbers x satisfying the given condition as an interval.       I 3x + 5 I &lt; 1

A: To solve the inequality: 3x+5&lt;1 Solution: We know that if x&lt;a then -a&lt;x&lt;a. We have…

Q: E and F are sets of real numbers defined as follows. E={y]y<1} F= {y]y<8} Write E UFand En F using…

A: The given question can be solved as shown in step 2.

Q: x-4 f(x) = In %3D x² – 5x + 6)

A: Given:  f(x)= ln x-4x2-5x+6⇒ f(x) =…

Q: F and H are sets of real numbers defined as follows. F = {w | w< 4} H= {w |w< 5} Write FU H and FN H…

A: Given F and H are sets of real number defined as followsF = W|W&lt;4H = W|W≤5We find F ∪ H and F ∩ H

Q: If h is defined by  h(x) = |X| + 2, What is the range of h if the domain of h is the interval…

A: The given function is h(x)=x+2

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r (x) = 3x s(x) =…

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Q: a) In the set of real numbers A = {x | | x - 2 | > 1, x E IR} cluster is given. Accordingly, express…

A: 1) A) The given set is: A={x||x-2|&gt;1,x∈ℝ} Here,  |x-2|&gt;1⇒x-2&gt;1 or x-2&lt;-1⇒x&gt;3 or…

Q: Suppose that the functions s and t are defined for all real numbers x as follows. s(x)= 3x-2 t(x)=…

A: The given function is: sx=3x-2tx=x-6  To write the expression for: t+sxt×sx  To evaluate the value…

Q: B and C are sets of real numbers defined as follows. B = {y|y> 1} C={y|y≤9} Write BUC and B n C…

A: Here, the given sets are: B=y|y&gt;1C={y|y≤9}

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) =x s (x) =…

A: Find s-rx as shown below: s-rx=sx-rx               =3x2-x3

Q: Is it true or fase ? There is a number c in the interval (a, b) such that f(c) = 0.

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Q: A and B are sets of real numbers defined as follows. A= {w |w<4} B={w |w26} Write AN B and A UB…

A: Given the subsets of real numbers A=w:w&lt;4 B=w:w≥6

Q: Use interval notation to represent all values of x satisfying the given condition. y = 2x - 11 + 3(x…

A: Use interval notation to represent all values of x satisfying the given condition. y = 2x - 11 + 3(x…

Q: E and F are sets of real numbers defined as follows. E = {w | w<3} EUF=- F={w |w<6} En F=E 3,65…

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