Suppose that the functions g and h are defined for all real numbers x as follows. g(x) = 6x h(x) = 4x+4 Write the expressions for (g-h)(x) and (g h)(x) and evaluate (g+h)(1). (g - k)(=) = [] %3D (g-A)(x) = [] (8 - 4)(1) = | %3D

Q: 1. Use the First Derivative Test with a number line to find the local extremes of the polynomial…

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Q: If g(x) = x2 + 3x - 1, find g(1), g(-1), g(3), and g(-4).

A: The given function is, gx=x2+3x-1. The objective is to find the values of gx at the points x=1, -1,…

Q: Find The value of K, to Continue The function X-2 f(x)= 4-JI4+X メ+23 - %3D メ=2

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Q: Given that f(x) = x² + 6x – 40 and g(x) = x +10, find f(x) + g(æ) and - express the result in…

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Q: Show that f(x) = x3 - 2x - 1 has a real zero between 1 and 2.

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Q: 2. Find the zeros of f(x)=x² -x-12.

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Q: 4. Find all real values of x such that f (x) = 0. 5x -8 f(x) = 9

A: Answer is x=8/5

Q: Find the constant a such that the function is continuous on the entire real line. 7sin x if x < 0…

A: Here we find the value of constant a

Q: True or False A polynomial function of degree 4 with real coefficients could have - 3, 2 + i, 2 - i,…

A: True or False  A polynomial function of degree 4 with real coefficients could have - 3, 2 + i, 2 -…

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

A: Given function is hx=1x+7x-3. To find domain. Solution: Domain of a function is the value of x for…

Q: Let ƒ(x) = x3 - x - 1. Use the Intermediate Value Theorem to show that ƒ has a zero between -1 and…

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Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: Find the constant a, such that the function is continuous on the entire real line. f(x) = {2x2,…

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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: What values of x would be found in the in the domain of function f(x)=10/x-2

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Q: Given that f(x)=x^2+3x-70f(x)=x2+3x−70 and g(x)=x-7g(x)=x−7, find (f-g)(x)(f−g)(x) and express the…

A: Given,

Q: If f(x) <0 for all real numbers x then f is decreasing or increasing on its interval?

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Q: If 4x-2x² <f(x) <x²–2x+3 for all real numbers except for x=1, then Selected Answers: limf (x) = 2 x…

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Q: 11. Find the domain of √√x-4 x² - 6x f(x)=

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Q: Graph the function with domain of all the real numbers: f(x) = 5 for x ≥ 3, and f(x) = -6 for x <…

A: Draw the line and the line on the cartesian plane.

Q: Find a rule for g-(x) if: g(x)=3x +2 %3D g(x)=| %3D

A: For finding inverse of the function g(x) replace x by y and g(x) by x and solve for y.

Q: Let ƒ( θ) = θ3 - 2 θ + 2.Use the Intermediate Value Theorem to show that ƒ has a zero between -2 and…

A: Intermediate Value Theorem: Let f(x) be a polynomial function then intermediate value theorem states…

Q: 21. Find the "natural" domain of the function f(x)= 4x-10x+4

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Q: Find the zeroes of the functions algebraically. x2- 14x+ 48 f(x)= 7x x = 8, x = 6, x= x= x =-8, x =…

A: Explanation of the answer is as follows

Q: Find the function f if it is known that f prime of x= 3x^2 +6x-7 and f(-1)=10.

A: Given: f'x = 3x2 + 6x - 7 and f-1 = 10 To find: fx

Q: 1) Which set of values for x should be tested to determine the possible zeros of the function f (x)…

A: We need to find possible x values that needs to be checked where function is zero.   NOTE - As per…

Q: Given that f(x)=x^2+3x-70 f(x)=x2+3x−70 and g(x)=x-7g(x)=x−7, find (f-g)(x)(f−g)(x) and express the…

A: Given data:     The given expression for the first function is: f(x)=x2+3x-70. The given expression…

Q: Suppose that 2 ≤ f '(x) ≤ 3 for all values of x. What are the minimum and maximum possible values of…

A: Given , Suppose that 2 &lt;= f’ (x) &lt;= 3 for all values of x. The minimum and maximum possible…

Q: Find a zero of f(x)=x-x³ by finding a fixed point of x= g(x)=x³.

A: we have to find the fixed point of g(x)

Q: Which polynomial function in standard form has a root of multiplicity 1 at x= 3, and a root of…

A: A polynomial function has a root of multiplicity 1 at x=3, and a root of multiplicity 2 at x=4

Q: find the domains and ranges of ƒ, g, ƒ + g, and ƒ # g.1. ƒ(x) = x, g(x) = 2x - 12. ƒ(x) = 2x + 1,…

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

Q: Examine the following quadratic function. f(x) = x² +22x - 114 Which statement is true about the…

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Q: What is g (x) - h (x) if h (x) = -3x and g (x) = 2x"? Put your answer in standard form.

A: Given: g(x)=2x2h(x)=-3x The objective is to find the value of g(x)-h(x)

Q: Show that f(x) = x5 +2x4-6x3+2x-3 has a solution between 1 and 2. Use the intermediate Value…

A: The equation given to us is  f(x) = x5 +2x4-6x3+2x-3

Q: 1. Use the Intermediate Value Theorem to show f(x)= 2x +6x² – 3 has a zero between a = -3 and b =…

A: I am attaching image so that you understand each and every step.

Q: Suppose the functions f and g are defined for all real​ numbers, x, as​ follows:   ​f(x)= -3x+12…

A: The given functions are: f(x)=-3x+12g(x)=2x2-18 The function fg(x) is another function obtained by…

Q: Prove that f(x)=4x-2^2x has at least one real zero in the interval [1,2] without actually solving…

A: The given data is: Prove that fx=4x-22x has at least one real zero in the interval 1,2 without…

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: If g(x) = √100 - x^2 , where - 10 ≤ x ≤ 0, find A) g^-1 (x) B) the domain and range of g^-1

A: g(x)=100-x2y=100-x2x=100-y2x2=100-y2y2=100-x2y=-100-x2 [here 0≤x≤10]g-1(x)=-100-x2 , 0≤x≤10

Q: Given that f(x)=x^2+3x-70 and g(x)=x-7g(x)=x−7, find (f-g)(x)(f−g)(x) and express the result in…

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Q: 1. When the function f(x) is divided by x + 2, the quotient is x2 -x -8 and the remainder is -3.…

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Q: Find all zeros. f(x) = x^4−x^2−30 f(x) = x^4+ 2x^2−15 f(x) = 3x^3−7x^2−7x+ 3

A: Since you have sent more than 3 sub parts therefore according to our policies we are bound to answer…

Q: Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of…

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Q: Find the critical number of f(x) = 3x^2 - 18x + 4

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Q: Show that for all real values of x, [(x-2)(x-4)] / 4x - 7 cannot take values between -1 and -1/4

A: Question: Show that the for all value of x                                    fx=x-2x-44x-7 can not…

Q: if 7+5i is a zero of a polynomial function of degree 5 with real coefficients, then so is

A: Given:   7+5i is a zero of a polynomial function of degree 5 withreal coefficientsWe know that  A…

Q: True or False The domain of 1f # g2 1x2 consists of thenumbers x that are in the domains of both f…

A: The domain of (f·g)(x) consists of the numbers x that are in the domains of both f and g

Q: Find an upper limit for the zeros of 2x4 - 7x3 + 4x2 + 7x - 6 = 0 5 4 -1

A: The given polynomial is  2x4-7x3+4x2+7x-6= 0

Q: Suppose that f(x) = [x² + g(x)]4. Suppose further that 9(-2) = -6 , g(5) g'(-2) = 5, and g'(-6) = 4.…

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