F and H are sets of real numbers defined as follows. F={v|v< 4} H={v]vs6} Write FO H and FUHusing interval notation. If the set is empty, write ø. (0,0) (0,0) (O.0) FnH = [0,0) Ø FUH = 00 -00 8.

Q: Let a, h, and k be arbitrary real numbers with a+0, and let f be the function given by the rule f(x)…

A:

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

A: The given function is: s(x)=x+2t(x)=3x2

Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

A: We know that Rolle's theorem  If y=f(x) is real valued function of a real variable such that  1)…

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:

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: 2) We will modify the domain to determine the set of occuring of |x| + 2, which will be the range.

Q: Determine the interval(s) on which x2 + 2x – 3 > 0. - Ох1 Ox 1 -3 1

A:

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

A:

Q: Let R; = {x E R|15 xs 1+ = 1, 1 + for each positive integer i. (Enter your answers using interval…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

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

A:

Q: Suppose that the functions S and t are defined for all real numbers X as follows. s(x)=x² t(x)=3x³…

A:

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

A:

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

A:

Q: Find the interval values for Z such that P(-z<Z<z)= 0.9886.

A: P(-z&lt;Z&lt;z) =0.9886.·.  x=1-0.9886         =0.0114

Q: Suppose that the function h is defined, for all real numbers, as follows. 1 x-2 if x 2 Find h(-1),…

A:

Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

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: If for a real continuous f(x), f(a) f(b) < 0, then in the range of [a,b] for f(x) = 0, there is…

A: It is given that f(x) is a continuous function and f(a)f(b)&lt;0. Then f(a) , f(b) have opposite…

Q: f x and y are two positive real numbers, then there exists a positive integer n such that ny>x

A:

Q: The domain of g(x) = 3 consists of all real x - 2 numbers except 2, represented in interval notation…

A: Given :          g(x) = 3x-2 To determine :              The domain of g(x) interval notation

Q: 5. Let f be defined for all real numbers and suppose f(x)-f(y)| ≤ (x - y)² for all real numbers, x…

A:

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…

A:

Q: Determine whether Rolle's Theorem can be applied to 22 –1 f (x) on the closed interval –1, 1. If…

A:

Q: Suppose that the function h is defined on the interval (-2, 2 as follows. -1 if-2<xs-1 if -1<x<0 0.…

A:

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

A:

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: If the domain of f is all real numbers in the interval [ 0, 7],and the domain of g is all real…

A: We know that if the domain of function f is a, b and the domain of function g is c, d then the…

Q: Find a function f and a real number a such that

A:

Q: Find functions f and g from the set of positive integers to the set of real numbers such that f (n)…

A: Here, we need to find functions f and g from the set of positive integers to the set of real numbers…

Q: For the given function f(x) and values of L, c, and ɛ>0 find the largest open interval about c on…

A:

Q: Z is the set of integers, R is the set of real numbers. 1. Functions f, g, and h are defined as f:R…

A:

Q: Suppose that the function h is defined, for all real numbers, as follows. -4 if x -2 h (x) = < 1 if…

A: Here the definition of a function is given and we have to find the value of function at given…

Q: For the given function f(x) and values of L, c, and e>0 find the largest open interval about c on…

A:

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: Define Floor: R → Z by the formula Floor(x) = for all real numbers x. Here are some example values:…

A: See the proof and counter example below.

Q: If f (x) = x2 + 2x -1, show thatf (x) satisfies the hypothesis of the Mean Value Theorem on the…

A:

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

A:

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: (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:

Q: 2. Determine whether Rolle's Theorem can be applied tof on the closed interval [a,b]. If Rolle's…

A: Here rolles theorem is applicable.

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: 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: 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 s (x) =x+1 1 (x)…

A:

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

A:

Q: Let the function f be defined by y = f(x), where x and f(x) are real numbers. Find f(2), f(−5),…

A:

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

A:

Q: 1 -Find all the points where f(2)is analytic. 2+3 Let /(2) =

A: