Express {x : 2 ≤ |x − 1| ≤ 6} as a union of two intervals.

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

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

Q: 4x² – 1 f(x) = 4. For which intervals is 2x2 – 3x – 2 continuous? What types of discontinuities are…

A: Given the function f(x) = 4x2-12x2-3x-2 To find the continuous on Intervals:- f(x) =…

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

A:

Q: 11. -6 -4 -2 0 2 4 6

A:

Q: the interval of differencing being unity. Ex Evaluate

A:

Q: 4 z+9 (z – 2) + 2 (9 – 2) < 18 (x + 1) Enter the exact answer in interval notation. -To enter 00,…

A:

Q: Choose the correct intervals of x and y such that (x+y) is greater than 8.

A:

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

A: 3x+5&lt;1

Q: In a class in which the final course grade depends entirely on the average of four equally weighted…

A: The solution is given below

Q: Prove that for x≠0 the inequality ex&gt;1+x holds.

A:

Q: Describe the set as a union of finite or infinite intervals. {x : |x2 + 2x| &gt; 2}

A: {x:x2+2x&gt;2}

Q: Show that the interval [a,b] is complete

A: Given

Q: Express the set of numbers x satisfying the given condition as an interval. |x| ≤ 9

A: Given: x≤9 Formula Used: z≤a, a&gt;0 then -a≤z≤a

Q: Find the largest open interval where 8. y = (x?_9)a° is increasing.

A: Given query is to find the interval where function is increasing.

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: Express the set of numbers x satisfying the given condition as an interval. |x + 7| &lt; 2

A:

Q: Find the largest open intervals where the function f(x) = O (-∞, -1), (-1, ∞) O (-∞, -1) none O…

A: We have to find the largest subset where function concave upward

Q: an be divided into two intervals (-∞, 1) an ne two intervals. rst consider the interval (-∞, 1). Let…

A:

Q: What is the intervals to its corresponding function which have at least one real zero. f (x) = 202 +…

A: Given query is to find the interval where function has atleast one real zero.

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

A: 4x-1≤8

Q: If h(x)= |x-4|+1 and k(x)=x2+3, which intervals contain a value of x for h(x)=k(x)?

A: Solve equation

Q: Express the following in interval notation. 3. 4 < x < 19

A:

Q: 13) Find the open intervals on which ƒ (z) = x³ – 12z is increasing or decreasing.

A:

Q: Show that there is a correspondence between the two intervals [0, 1) and [0,1].

A: Given interval 0≤x&lt;1 is a subset of  0≤x≤1. In this situation ,there is an obvious injective…

Q: state all intervals of x where f(x) is increasing.

A: TO FIND INTERVAL WHERE f(x) is INCREASING FIND f '(x) and see interval where f '(x) &gt;0 f(x)…

Q: o Yes, zero is contained in the interval.

A:

Q: 1. dt 1+1? (Use 8 intervals) 3.

A:

Q: 4. Describe the intervals on which each function is continuous. a) f(x) = 3x5 – 5x2 – 1 - 1 b) g(x)…

A:

Q: In a class in which the final course grade depends entirely on the average of four equally weighted…

A: Given  Charles has scored 93 ,82, and 87 on the first three test. Average of four equality weight…

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: Prove that for x&gt;0 the inequality 1+2lnx≤x2 is true.

A: Inequality given in the question is: Consider the function; f(x) = 1+2ln(x)-x2 Let us find critical…

Q: Express the set of real numbers between but not including 2and 7 as follows.(b) In interval…

A: given: 2&lt;x&lt;7 given expression in interval notation can be written as below x∈2,7

Q: Express the set W = {x | |x| < 3} using interval notation. %3D

A:

Q: Determine over what intervals f(x) &gt; g(x)

A: Given the graph of two functions f(x) and g(x). Here f(x) is a parabola and g(x) is a line.

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: Prove the inequality √1+x≤1+x2 for x&gt;1.

A: Consider the function. Find its derivative.

Q: The interval notation for the set (xlx ≤4 or x>-2} is. [-2,4] A O (-2,4] BO R .CO DO [-2,4) EO…

A:

Q: - Give the domain for k(a) in interval notation. x2 + 3x +2

A:

Q: on is discontinuous on the specified interval. Vx2 - 64 if IS -8 if-8<x<8 88] 0 ifx28 f(x) = {x+8

A: If a function is continuous then the left hand limit, right hand limit and value of function at that…

Q: Express the set W = {r|x < 2} using interval notation. %3D

A: W={x | x&lt;=2}

Q: a) Verify Rolle's Theorem for ƒ(x)= 2.x' – 8.x + 4 over the interval [0,2].

A:

Q: Show that the interval [0, 1] is uncountable.

A:

Q: Use interval notation to represent all values of x satisfying the given conditions: y = 7 - lx/2 +…

A: y=7-x2+2

Q: Express the interval using two different representations. -10 -8 -6 -4 o 2 4 8 o 12 -12 10

A: A graph with blank dot at x=6 and move towards right. Concept When we use a blank dot, it means that…

Q: find the positive intervals for  x2 − 3x

A: We need to find the interval for which function is positive .

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: Show that f (r) = x³ – 3x2 + 2 is monotonically increasing on every interval.

A: Given that: f(x)=x3-3x2+2

Q: 32 (c) Show that Hence, find the interval for x that satisfies the inequality = 22* 2 x 4" 32" -…

A:

Statements and Logic

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