Express the function G in the form f.g.h. (Enter your answers as a comma-separated list. Use non-identity functions for f(x), g(x) and h(x).) G(x) = (6 + vx (f(x), g(x), h(x))- 16+x*

Q: Find the constant a such that the function is continuous on the entire real line. 7sin x 0 = g(x) =…

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Q: Consider the functions f(x) = x +7 and g(x) = 27 - x2. (a) Use algebra to find the x-values where…

A: f(x) = x+7g(x) = 27 -x2calculating intersect points :f(x) = g(x)

Q: Let f(x) = x -9, g(x) = /x + 9, and h(x) = 6x² - 9. Find the rule for the function. %3! gh f

A: Since, f(x)=x-9, g(x)=x+9 and h(x)=6x3-9.Our Aim is to find the rule for the function ghg-f.

Q: x+5 4. f(x) = %3D x2-5x+4

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Q: g(x) = e2" + x² – 2 with R>0 - 2²

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Q: Find f + g, f - g, fg, and f/g and their domains. f(x) = 5 - x,    g(x) = x2 - 3x

A: Given, f(x)=5-x  and g(x)=x2-3x To find  f+g, f-g, fg, f/g.

Q: The function h(x)= 1 over x-8, can be expressed in the form f(g(x)), where g(x)= (x-8) , and f(x))…

A: use composition of function to find the function f(x).

Q: Let f and g be the functions defined by f : R → R+ ∪ {0} with f (x) = x2 and g : R+ ∪ {0} → R with…

A: (fog)(x) is the value of the function f(x) at g(x) (fog)(x)= f(g(x))

Q: Find the domain of the function : g(x) =1/(x2 + 1) - 1/(x2 - 1).

A: The domain of  rational function is the set of all real numbers except those for which the…

Q: 6. Determine all values of x at which the function is discontinuous. x2- 2x +5 f(x) = x2-4x 0, 4 O…

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Q: Find the value of c such that the function is continuous on the entire real number line. [x + 3, xs2…

A:

Q: Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = 1x. Find the functions. f (x) + g(x)

A: Since, we have been given that:-f(x)=x2-2x -(i)g(x)=3x-1 -(ii)and h(x)=x -(iii)Our Aim is to find…

Q: 3 3 Find the functiong such that fo g= V6x -2 if f(x) = /x g(x) =

A: topic - functions

Q: Find the absolute maximum and minimum of the function f (x) = x³ - x+2 on the interval [0, 3] %D

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Q: Find f + g, f - g, fg, and f/g and their domains. f(x) = x, g(x) = 2x

A: The given functions are: f(x) = x, g(x) = 2x The sum of these functions is given by: f(x)+g(x)=…

Q: Let f(x) = x²-1 and g(x)= V15 – a Find the the natural domain o the function gof(x)

A: we have to find domain

Q: The graph of function f(x) = x³ – 6x² + 9x + 1 is - concave upward on O (-∞0, 2) O (-∞, ∞0) O (2,…

A: The given function is: f(x)=x3-6x2+9x+1

Q: 7 Find the most general function F such that F'(): - 5V?.

A:

Q: The range of the function f (x) = 2+ V9 – x² is [2, 5] O [0,3] О -3, 3] O [-1,2] O [-3,0]

A: Explanation of the answer is as follows

Q: Find f+g, f-g, fg, and f/g and their domains. f (x) = /16 – x², g (x) = V/x² – 1

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe-x²/98…

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Q: 3. Determine whether x = 2 is the x coordinate of an extremum of this function: %3D f(x) =- 1 x³ +…

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Q: Find all values of x for which the function f(x)=(x^2+x-6)/(x^2-5x+6) is not continuous.

A: We will solve the problem.

Q: determine all values of x at which the function is discontinuous: 1. f(x)=2x/(x^2-1) 2. f(x)=…

A: Given function is  fx=2xx2-1 The function fx is undefined when x2-1=0 which gives x=±1. So, the…

Q: Let f(x) = Vx +7 and g(x) = x +3 a) Find (2) (2) show work. b) Give the domain of the function (-)…

A:

Q: 7. If f(x)=4x-3 and h(x) = 4x² -21, find a function g such that fog=h

A: The given functions are: fx=4x-3 and hx=4x2-21

Q: Suppose that f(x) is a differentiable function such that f(3)= 8 and f'(3)=-2. If g(x)=xf(x), then…

A: Product Rule of differentiation : d(u.v)dx = u.dvdx + dudx.v

Q: Let f(x) = x3 + 3, g(x) = x2 - 3, and h(x) = 3x + 3. Find the rule for the function. fgh

A: Use the rule of composite functions.

Q: Please show step-by-step solution

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Q: let f(x) = x-5 / x2+x -12 and g(x)= x+3 / 3x+12 find an equation of the funtion f-g

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Q: Let f(x) = √20- x and g(x) = x² - x. Then the domain of fo g is equal to

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Q: form the graph of f(x) into th 5) f(x) = x³ g(x) = -(x – 2)° %3D 3 %3D

A: We have to find

Q: 7. Find the domain of the functions. a. g(x) = 4 +x – V3 – 5x. 7x3-x²+16 b. f(x) х2-21х-100 In(7-3x)…

A: 7 a Given function is : gx=4+x-3-5x For function gx to be defined if , 3-5x≥0-5x≥-3x≤35   Thus , the…

Q: Find the domain of the function. g(x) = In(x - x2)

A: The domain is the set of values for which the function is defined or gives a real number as an…

Q: 39. Let f(x) = 2x3 - 4. Find a function y = g(x) so that (f o g)(x) =x+2.

A: We use the definition of composition of functions to find y= g(x).

Q: Let f(x) = x + 6, g(x) = x2 - 10, and h(x) = 3x + 5. Find the rule for the function. %3! %3D f-g

A: given: fx=x3+6g(x)=x2-10h(x)=3x+5 we have to find a rule for the function f-g

Q: Let h(x) = f(x)g(x). If f (x) = 3x² – x – 4 and g(x) = -x² + 2, what is h' (-1)?

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Q: The function h(x)=1x+7h(x)=1x+7 can be expressed in the form f(g(x))f(g(x)) where…

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Q: 3. Find (f-g)(x) if f(x) = 22 +x+1 and g(x) = x2- r - 1. %3D %3D

A: Given, f(x)=x2+x+1g(x)=x2-x-1

Q: Let f(x) = x − 9 and  g(x) =square root of x+9.  Find the rule for the function. gf

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Q: Let h(x)=f(x)g(x). If f(x)=2x2+1,g(1)=0, and g′(1)=−1, what is h′(1)?

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Q: Express the function,h(x) = (2x - 5)3 as a composition of two functions f and g so that h(x) = (f ∘…

A: Given, hx=2x-53

Q: let f(x)=-2x^2-x, and let g(x)=f(x)-f(-1)/x+1, x not equal to -1. find g(10).

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Q: Find and sketch the domain for the function. f(x,y) = / (x2 - 9) (² -4) %3D

A: This is the problem of the domain of a function of several variables.

Q: Find F as a function of x and evaluate it at x = 2, x = 5, and x = 8.

A: Consider the given: Fx=∫1x20v2dv Find the…

Q: Let h(x)=f(x)g(x). If f(x)=x^2+4x−1,g(−2)=3, and g′(−2)=−5, what is h′(−2)?

A: We have to find function

Q: Find the constant a such that the function is continuous on the entire real line. x² - a² if x * a…

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Q: Express the function,h(x) =1/(4x + 5) as a composition of two functions f and g so that h(x) = (f ∘…

A: here given as hx=fogx=14x+5