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

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

A: x-9x2-9

Q: A(n) ______ ____________, denoted [a, b], consists of all real numbers x for which a ≤ x ≤ b.

A: It is known that any closed interval a, b can be represented as an inequality a≤x≤b.

Q: Find all values of c such that the domain of is the set of all real numbers.

A:

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 <…

A:

Q: Given the domain and codomain of set of all real numbers, categorize the ff.: f (x) = 2x³ – 4…

A: Given - The domain and codomain is the set of real numbers. Function given is f(x)=2x3-4 which can…

Q: If a,b,c,d are in distinct real number in A.P. Such that 2(a-b)+c(b-c) +(c-a) =2(a-d)+(b-d) +(c-d)'…

A:

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

A:

Q: B and C are sets of real numbers defined as follows. B={w | w>1} C={w|w>6} Write B U C and B N C…

A:

Q: Prove that the value of an expression (a - 1)(a - 3)(a - 4)(a - 6) + 10 is positive for every a…

A: To prove that   the value of an expression (a - 1)(a - 3)(a - 4)(a - 6) + 10 is positive for every a…

Q: If n is any real number and f(x) = x", then f'(x) = nx"-!

A: Why does ddxxn=nxn-1                 ddxfx=limh→0fx+h-fxh…

Q: Given any two distinct real numbers, there is a real number in between them.a. Given any two…

A: It is given that any two distinct numbers there is a real number between them.(a)The two distinct…

Q: R.4. Prove that the set of real numbers in the interval (0, 1) which have a terminating decimal…

A:

Q: Given that |f'(x)| < 1 for all real numbers x, show that If(x1) – f(x2)| < \x1 – x2| for all real…

A:

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: Let æ be a real number. Show that [3r] = [a] + æ + + 3

A: Here we have to show that 3x=x+x+13+x+23

Q: find all real such that 12x-11>x

A: The inequality can be calculated using absolute values. The absolute value function takes a positive…

Q: Let x be a real number. Prove that x is an integer if and only if [0.891a] + [0.109æ] =

A: Solution: Definitions floor function: It takes real number x as an input and gives as output the…

Q: Given f(x)= Vx– 5;x+5 and g(x)=x +3. Find the domain of (gof)(x)? | All real numbers greater than 5.…

A:

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: 10. Let x be a real number. Prove that at least one of the numbers /2 – x or /2 +x is irrational.

A:

Q: A and B are sets of real numbers defined as follows. A={x|x≥1} B={x|x&gt;7} Write A∪B and A∩B using…

A: Definition used:Union of two given sets is the smallest set which contains all the elements of both…

Q: State all integer values of x in the interval 1 2

A: Given inequality is -x+4≥2 and the given integral is 1≤x≤8 we have to state the integer values of x…

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: 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: Find the domain. f (x) =1 3 - X O {x[ x is a real number and x < 3} O All real numbers O {X[ x is a…

A:

Q: State all integer values of x in the interval 3 -7

A:

Q: For any integer m and any real number x, if x is not an integer, then [x]+[m- x] = m- 1.

A: Given that m is an integer and x is a real number which is not an integer. we know that for any real…

Q: x-4 f(x) = In %3D x² – 5x + 6)

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

Q: 1. Use the Intermediate Value Theorem to show that there exists at least one solution in the set of…

A:

Q: 1 The domain of h(x) = - + 7 consists of all real numbers except 0 and 3, represented in interval…

A: Consider a function fx. The domain of a function fx is those values of x for which the given…

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

A:

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: 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: 17. Let a and b be real numbers with a 0, the number x belongs to the open interval (a – €, b + €).…

A: Given that a and b be real numbers with a&lt;b, and x be a real number. Let for each ε&gt;0, the…

Q: For every real number x+1, n-1 1+x+x² +x' +. x´+x' +...+x" for all neN. 1-x

A: The question has a mistake , as in the R.H.S the power of x must be (n+1).

Q: Prove that if a and b are real numbers with a < b, then there are infinitely many rational numbers…

A:

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: Let the universal set be the set R of all real numbers and let A={xeR|-2<x<2} and B= {xeR|-3<x<1}.…

A:

Q: Suppose x is a real number and x is not equal to zero. Prove that if ((x^1/3)+5)/((x^2)+6)=1/x, then…

A: Given that, x is a nonzero real number, and 8 is not a root of given equation.

Q: If x is any real number, then

A:

Q: f(x) = x+3x−2x+3x−2 and g(x) = x−1x+1x−1x+1 . The domain of f ∘∘ g is the set of all real numbers…

A: Use fog(x) =f(g(x))

Q: Suppose x is a real number and x + 0. Prove that if then x 7 8. 2 16

A:

Q: . The operation * is defined over the set R of real numbers by a *b = a+b+2ab. What is the identity…

A: We will find out the required value.

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

A:

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

A:

Q: For all numbers x , x4 >x true or false

A: Given, All number x We have to find Whether    x4 &gt;x        is true or false

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.