B and C are sets of real numbers defined as follows. B-x |x<2} c={x |x27) Write Bn Cand BUC using interval notation. If the set is empty, write Ø. Bn C = || (0,0) [0,0) 可 (口可 (0,0) %3D [0,0) BUC =| %3D - 00 8.

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: Use interval notation to represent all values of x satisfying the given conditions: y = 1 - (x + 3)…

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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: To show that ( n + a ) b = θ ( n b ) ( n + a ) b = θ ( n b ) for any real constants a a and b b…

A: Here we use the binomial expansion:

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: (2) The floor function is defined as a| = max{m e Z|m < x}. Effectively, the floor function is the…

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Q: Use interval notation to represent all values of x satisfying the given condition. y = 1 - (x + 3) +…

A: y=1-x+3+2xy is atleast 4 i.ey≥41-x+3+2x≥41-x-3+2x≥4

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

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Q: The domain of h(x) 7 - consists of all real numbers except 0 and 3, represented in interval notation…

A: Given function is hx=1x+7x-3. To find domain. Solution: Domain of a function is the value of x for…

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: 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: Let S be the set of all real numbers except -1. Define * on S by a*b = a + b + a b. The solution of…

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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: C and D are sets of real numbers defined as follows. C={v|v>4} D-{v| v

A: C ∩ D those element contained in both C and D. C U D those element contained either in C or D

Q: C and D are sets of real numbers defined as follows. c=%=|z<1} Write CND and CUD using interval…

A: Given that

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) =x s(x) = 3x²…

A: givenr(x)=x3s(x)=3x2(s-r)(x)=s(x)-r(x)=3x2-x3      answer(s.r)(x)=s(x)r(x)=3x2.x3=3x5     answer

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: Let c, a, ß be nonzero real numbers such that e + B. Find a given that 2n-3 ac 11 c - B'

A: Given, c,α,β be nonzero real numbers such that c≠β, To find the value of α such…

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: 19. Which of the following properties of Real Numbers is NOT true ? * a. Vx ER, x+0 = x b. Vx, y, z…

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Q: Find the Domain of 1, if f(=) 0(s-6) %3D O Domain: y is all real numbers O Domain: y N0 O Domain: NO…

A: Given f(x)=6(x-6)2 To find f-1, assume y=f(x) then swap variables to find f-1

Q: c and d are sets of real numbers defined as follows. c={y]y<3} D={y]y<9} Write cn D and cUD using…

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Q: Let r and s be nonnegative real numbers, f(r) = r" and g(r) = r. %3D Find all pairs r and s such…

A: Given that: f(x)=xr           and             g(x)=xs

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

A: Given : rx = x + 6sx = 4x + 4

Q: The function f(x) = 4 for x<2 and f(x) = 4 for x2 2 has domain of all the real numbers. True O False

A: The given function is a constant function. We find it's domain by using the definition of domain of…

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

A:

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) = 4x+1 s (x)…

A: Given : The functions r and s are defined for all real numbers x as r(x) = 4x + 1 s(x) = 3x   To…

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: 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: Let R+ = {x € R|x>0} be the set of positive real numbers. Let A = [a,b), a,beRb +00, be an (right…

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

A: Given  rx=6xs(x)=2x+3 where the expression for r+sx,  r-sx  and  r·s2 is to be evaluated.

Q: Example: Given m(x) = x + 3 , n(x) = x² – 9 , and p(x) = Vx + 1 %3D - Find (n-m) (x) and write the…

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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: 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: A and B are sets of real numbers defined as follows. A={v| v7} Write A N B and A U B using interval…

A:

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: If an inflection point of the aurve f(x)=acos(2.x) +bsin(3x) is P(z/6,5), then what are the real…

A: At inflection point :   d2dx2fx=0d2dx2acos2x+bsin3x=04acos2x+9bsin3x=0

Q: 3. Given that fæ) is continuous for all real numbers, find the value of "a" & “b". 2ах + 3b , х<1 =…

A: It is known that if function is continuous for all real numbers, then left-hand limit and right hand…

Q: F and H are sets of real numbers defined as follows. F={v|v<4} H={vI vs아} Write Fn H and FUH using…

A: Given, F={v|v&lt;4}H={v|v≤6}

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) 3x + 1> 2x OR 3x + 1 2x AND 3x + 1 < 5x – 2.

A: 3x+1&gt;2x  or   3x+1&lt;5x-23x-2x&gt;-1 or 1+2&lt;5x-3xx&gt;-1 or  3&lt;2xx&gt;-1 or…

Q: E and F are sets of real numbers defined as follows. E={x|x&lt;1} F={x|x&lt;7} Write EUF and E∩F…

A: We have Sets E={x|x&lt;=1} and F={x|x&lt;7}.So , first we will plot the number line for given sets.…

Q: e and F are sets of real numbers defined as follows. E={v| v7} Write EUF and ENF using interval…

A: Note that: Union of two sets contains all the elements present in both the sets and intersection of…

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 = {x | xs 3} F = {x | x > 6} Write EN F and E…

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