8. The domain of - consists of numbers x for which g(x)_0 that are in the domains of both – and,

Q: 4. [5] Please find in interval notation the values of x for which this expression is real. Show…

A:

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

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…

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Q: 3 If f(x) = 2 + x, evaluate Σƒ (k+1). atas (k k=1

A:

Q: Express x^8-x over 2[x] and over F2[x] as a product of irreducible

A:

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

A: 3x+5<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: 2) We will modify the domain to determine the set of occuring of |x| + 2, which will be the range.

Q: 2) (a) Verify that the function f(x) =x3 – 3x + 2 satisfies the hypotheses of the Mean Value Theorem…

A: to verify the Mean value theorem over interval [-2, 2] for following functionf(x)=x3-3x+2

Q: 4 if x3 to define f at x = -2 in such a way that f becomes continuous nossible what ie the velue of…

A: We have to find the following conditions according to the given information

Q: Let g : Z----Z be given by g(x) ={x                if x is even.…

A:

Q: 6 2, find the following. - V (gof)(x) 2√2(1-2x) X (b) the domain of (gof)(x) in interval notation −…

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Q: 5. Check the continuity of r+5| 2x+10 x + -5 f(x) = x = -5 at x = -5.

A:

Q: If f(x) = prove that f (x) is an even fun %3D et-1 2

A: Introduction :

Q: 3.11 If a real-valued function f defined on the real line is monotone nondecreasing or…

A: It is given that,  f is a real valued function defined on the real line and f is monotonic. We have…

Q: 8.26 Show that the IVP x" = –6x(x')³, x(-1) = -1, x'(-1) = , has a unique solution x and find the…

A: Given IVP is x''=-6x(x')3 , x(-1)=-1 ,x'(-1)=13

Q: 1 Expand f(2) = -in the domain 4 < |2 < 12 (z-4)(z–12)

A:

Q: 39-40 Show that / is continuous on (-*, *). if 1 39. (x) -

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Q: If f(x) has odd degree and negative leading coefficient, as x goes to -∞, then f(x) would go to

A:

Q: Prove f:N - N. F(X) = 5x is injoctive.

A:

Q: In(2) ith(7-32) + vr² + 1. Answer using interval 3. Find the domain of the function f(x) = + In…

A: In our function three expression added together. Hence we going to see each expression separately…

Q: If x>-I show Hhat Cl+x)> \+nx ,H

A:

Q: Present a combinatorial argument to justify your answer. How many functions are there from {1, · · ·…

A: Consider the given information as, 1,⋯,n to 0,1

Q: 9. Use the given graph of f (x) x2 to find a number 8 such that %3D if |x – 1| < 8 then |x2 – 1| <;…

A:

Q: 1. Let f:R R be defined by {1 if x rational number, 12 if x irrational number f(x) = Show that f is…

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Q: if ニ if 1-X fCx +2) = f(x) Hx f on [-3,3] and we Suppose draw the funch'on

A:

Q: 8. What is the value of c guaranteed to exist by the Mean Value Theorem if m(x) = x4 - 3x over the…

A: The answer for the above question is as shown below.

Q: Find the domain of the function. h(x) = In x + In(2 - x)

A: Given h(x)=ln x+ln (2-x) Find the domain by finding where the expression is defined.

Q: Suppose that f(2) = 16 and that f (x) 2 - 3 for allx in the interval [2,7]. Determine the smallest…

A: Follow the procedure given below.

Q: 6. Determine all functions f analytic in |2|< 1 and satisfying ƒ(²-) = k+k² 1+k2' k = 2,3,4,...

A: We have to determine all the analytic functions f  in  z&lt;1  such that  f1k = k+k21+k2 ,  k = 2,…

Q: Find the number of all onto functions from the set {1, 2, 3, ... , n} to itself.

A: Consider the given set {1, 2, 3,…, n}Since the function is onto. So, all elements of {1, 2, 3,…, n}…

Q: Q 4. (a). Show that limit *1, does not exist if (5-4x S(x)=. -)- {ax-2 for x <1] for xz1]

A:

Q: express the set of the numbers x satisfying condition |x-1| &lt; 18 as an interval

A: The condition |x-1|&lt;18 is rewritten as,

Q: 5. Show that Ax) = Inx² - 1- In/3, if f'(x)= and (2) = 0. x- 1 Justify your answer.

A: To show that f(x)=ln|x²-1|-ln√3

Q: (х — т 11- тх if x < 3 if x 2 3 5) Find m so that g(x) = Is continuous for all x?

A:

Q: 5. Show that if X~F.m, then X-1 ~Fm.,

A: The probability density function of a random variable X:It is given that the random variable X…

Q: Which function has a domain consisting of real number Ax) = X+ 25 1 Ax) = x + 25 1 Ax) = x* - 25 1…

A: To find: function with domain all real numbers.

Q: Find the extreme values of f(x) = In 1+x SOUITION

A: Given- fx=lnx1+x2 To find- The extreme value of the above function.

Q: A³ f2 = V³ fs 3

A:

Q: 3. Determine the value of a so that f(x) is continuous on the entire real number line when: f(x) =…

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Q: 6. Prove from first principles (with ac- 6 argument ) that लेग ½ lim 7--1

A: 1x2+1-12=2-x2+12x2+1                               =2-x2+12x2+12+x2+1…

Q: Find all numbers, c, that satisfies the Mean Value Theorem for f(x) = x3on [1, 4].

A:

Q: Show that lGl =20 , so G is not simple

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Q: 8. 7 If f(x) = and g(x) = - , %3D x²-x-2 find (f- g)(x) and determine any domain restrictions x2+x-6

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Q: 5. Find three relation from {1, 2} to {6, 7} that are NOT functions.

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: set of integers is denoted by Z

A: There is some standard notation for certain types of sets . Set of real numbers is denoted by R,…

Q: Suppose that f(2) = 16 and that f'(x) 2 - 3 for all x in the interval [2,7]. Determine the smallest…

A: This question is based on Mean value theorem.

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A:

Q: 8. Determine the domain of the function and express in interval notation Ax)

A:

Q: 28. Graph of f" 2+ -1 2 3 4 5 +x+ 5 -4 4- 5. test to determine the local 2.

A: Graph

Q: 5 + x, if -T <x<0 - x, if 0<x < A f (x) ||

A: