Express the following in interval notation. {x | 4

Q: Suppose that the function h is defined, for all real numbers, as follows. if x+0 1 if x=0 Graph the…

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Q: Find the domain of the function ∑ akzk from k = 0 to k = ∞

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Q: Find three intervals on which ƒ is one-to-one, making each interval as large as possible.

A: We will cut the function at the critical points.

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: Find the domain of f(x)=x² for 0<x<5. O (1,25] O (0,25) O [0,25] O [1,25)

A: Given: The function is fx=x2 for 0≤x≤5. To find: The domain of the given function. The given options…

Q: For each function h given below, find a formula for h(x) and the domain of h. Enter the domains…

A: Given data: The given function is f(x)=(7x-7)1/2. The second function is g(x)=8x2-6. (A) The…

Q: Describe the set as a union of finite or infinite intervals {x : Ix - 4 I &gt; 2}

A: x:x-4&gt;2

Q: In the given question/s, let f be a function that is positive and differentiable on the entire real…

A: Given, g(x)=f(x) Let f be a function that is positive and differentiable on the entire real number…

Q: Choose the correct intervals of x and y such that (x+y)³ is greater than 8. O A O B x> or y > Oc y>…

A: Y’’ +4y’+ 5y=35 e-4x      y’(0)=1  --&gt; i) Therefore, (D2+ 4D +5)y =0 is homogenous The auxiliary…

Q: Given the graph of the function f(x) = In(x²) – 2 on the interval [-10, 10]. %3D y -10 -5 5 10 X Use…

A: The definition of absoulte function is x=  -xwhen x&lt;0xwhen x≥0We need to write the functionlnx2-2…

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: Exercises 1–10: Express the following in interval notation. 1. x < 2 3. x 2 - 1 5. {x | 1 s x < 8}

A: 1. x&lt;23. x≥-15. x|1≤x&lt;8

Q: Find four intervals on which f is one-to-one, making each interval as large as possible.

A: Given: To Find: Four intervals in which the function is one-to-one.

Q: Write the set of points from -2 to 2 but excluding 0 and 2 as a union of intervals:

A: To Find: Set points from -2 to 2 excluding 0 &amp; 2 as union of intervals.

Q: Given the function f(x) = -2x - 16x – 36x2, determine all intervals on which f is both increasing…

A: Given fx=-2x4-16x3-36x2

Q: - whether the following relation is a functio- x² – 2x + 1

A: We have to identify  the given  relation is function  not

Q: If h is defined by h(x) = lxl + 2 a) what is the range of h if the domain of h is yhe interval…

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Q: Give the domain of f, the domain of g, and the domain of m, where m(x) = f[g(x)]. f(u) = In u;…

A: Given:  A  function  fu=ln u; gx=2x  mx=fgx To Find: Domain of f, g, m Domain is the set of all the…

Q: List the open interval(s) on which f

A: Given, the graph of the function is

Q: Describe the set S = { x : I 1/2x - 3 I &gt; 4} in terms of intervals.

A: S=x : 12x-3&gt;4

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: Describe the set as a union of finite or infinite intervals { X : I 2x + 4 I &gt; 3}

A: Given set is x:2x+4&gt;3

Q: Find a set of four integers such that their order and the order of their absolute values are the…

A: We have to find a set of four integers such that their order and the the order of their absolute…

Q: Use the given graph of the function f(x) to complete the statement. 4. 3- -3 -2 -1 3. -11 2 -1 - 00…

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Q: Q1. Describe and diagram the intervals determined by the following inequali 1. -3 < x < 5 2. 2 <x<6…

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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 f(x)=3x−3, g(x)=sqrt(2/x-3) and h(x)=2/x find h o f and its domain. Write answer in interval…

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Q: Use the mean value theorem to establish the following inequalities: a) e* > 1 + x for x > 0

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

A: Given function is hx=x+2 Graph of the function can be drawn as,

Q: The domain of the function fod- tanh(17-) is (A, 198), Then The value of k- The value of A=

A: Let us consider the given function f(x)=tanh-1x The domain of the function is  x∈(-1,1) The range of…

Q: without making use of any absolute value symbol. ) Give the set S of all possible values of y if v =…

A: Please view next step for details

Q: Find the values of x such that |2x + 7| < 0.01. The values of x that satisfy |2x + 7| <0.01 are…

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Q: Suppose that the function h is defined, for all real numbers, as follows. --x+5 if x #1 h(x)= 31 -3…

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Q: Suppose that the function h is defined, for all real numbers, as follows. --x²+5 if x # -1 h(x)=< 4…

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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: If the function f is continuous for all real numbers and if f (x) = when z# -2, then f (-2)= -4 B -2…

A: we will use the fact that f is continuous for all real numbers and hence we will use the definition…

Q: For each of the following relations, give the domain and range, and indicate which are…

A: Given, relation is 3, 5, 5, 7, 7, 3. Domain is the set of x values for which function is defined. In…

Q: Describe the set as a union of finite or infinite intervals.  {x : |x 2 -1 | &gt; 2}

A: can be written as x^2-1&gt;2 or x^2-1&lt;-2

Q: Find the open intervals on which f(x) = x3 − 3/2x2 is increasing or decreasing

A: Find the open intervals on which f(x) = x3 − 3/2x2 is increasing or decreasing

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

A: Set: In set builder notation the real number between 2 and 7 but not including both the numbers, Let…

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: Is this set finite or infinite? {x € R|1 < x < 2}

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Q: Describe the set S = { x : I } x - 3 I &gt; 4} in terms of intervals.

A: S=x : x-3&gt;4 Now consider, x-3&gt;4⇒x-3&lt;-4  or  x-3&gt;4   ∵x&gt;a⇒x&lt;-a  or  x&gt;a⇒x&lt;-1…

Q: Given the function f(x) = -x – 8x3 - 18x² , determine all intervals on which f s both increasing and…

A: For a function f(x) to increase in an interval at each point the condition is : f'(x) &gt; 0.

Q: Given the function f(x) = -x³ + 5x*, determine all intervals on which f is both increasing and…

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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: Given the function f(x) = 2x – 16x³ + 36x², determine all intervals on which f is both increasing…

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Q: Give the domain of each of the following functions in interval notation. 6. s(x) = 1+ x² 6. k(x) 1 –…

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Q: the domain cant be x >3? its a union of intervals?????

A: fx=-3x+1 and gx=x-3