Find the rules for (fog)(x) and (gof)(x) and give the domain of each composite function. f(x)=x²,g(x)-/1-x (fog (x)= the domain of (fog)(x) is : Example: x<-3; 37 (gof)(x) = the domain of (gof)(x) is : Example: x<-3; 37

Q: What is the value of g(x) when x = 3 in the piecewise function, g(x) = x2 + 1 if x > 3 and g(x) =…

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Q: Find the domain of the function. G(x) = x + 4 / x3 - 4x

A: we have to find the domain of the following,  G(x)=x+4x3-4x

Q: Differentiate the function. g(x) = In(xe-8x) g'(x) = %3D

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Q: Find bn if the function f(x)=x^2.

A: bn-fx=x2 Fourier series of                     fx=x2   is                     fx=902+∑n=1∞an…

Q: Find the constant a such that the function is continuous on the entire real line. - [8x², a = ax -…

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Q: Let g(x) = -x2 + 4x - 5, Find g(a)

A: Consider: gx=-x2+4x-5. Find ga To evaluate ga substitute x with a in gx=-x2+4x-5.

Q: Find f + g, f - g, fg, and f/g and their domains. f(x) = x2 + 2x,    g(x) = 3x2 - 1

A: Given functions are fx=x2+2x,gx=3x2-1. f+g=x2+2x+3x2-1=4x2+2x-1 Domain of f + g is -∞,∞.

Q: Let f(x) = x2 - x - 4 and g(x) = 2x - 6.Find (g - f)(x).

A: Given

Q: Let f(x) = x2 - x - 4 and g(x) = 2x - 6.Find g(f(-1)).

A: Given:

Q: Differentiate the function. g(x) = (3+2x)/(7-8x)

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Q: Use the Leading Coefficient Test to determine the end behavior of the graph of f(x) = x* – 4x?.

A: To Determine: use the leading coefficient test to determine the end behaviour of the graph of f(x).…

Q: Find the domain of the function : g(x) =2/(x2 + x - 12)

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Q: Use the function f(x)=3x2-5x, g(x)=6x-4,h(x)=5-x3 to find the following (h-g)(x)

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Q: Use the functions f(x) = x − 3 and g(x) = x³ to find the value or function. (g-¹ of ¹)(-3) (g-¹ of…

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Q: Find the domain of: f(x) = x2 - x + 5

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Q: Explain why both f (x) = x/ (1- x4) and g(x) = p are algebraic g(x) = -x / √(1-x4) functions.

A: f(x)=x1-x4 and g(x)=-x1-x4

Q: Find the domain of the function.

A: The given equation is qx=2+x3-x.

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(x) = 2x3 - 4. Find a function y = g(x) so that (ƒ ∘ g)(x) = x +2.

A: To find the function y= g(x).

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: Differentiate the function. g(x) = 2x2 – 2-8x + 11 g'(x) =

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Q: бх + 6 Determine the domain of f(x)= x²- 6x

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Q: • The domain of f(x) = 3-x is x2 -1 %3D

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Q: Show that the function f (x) = -x3 + 2x2 - 6x + 3 is always decreasing.

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Q: Determine the end behavior of the function f (x) : x³ + 3x2- x - 3

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Q: Differentiate the function. g(x) = (x8 − 6x)−2

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Q: Determine the number of possible positive and negative zeros for the given function in accordance…

A: To determine the number of possible positive and negative zeros of the function.

Q: Find a rule for g(x) if: g(x)=4-5x

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Q: Find the domain of the function: g(x) = (3x + 2) / x2 - 2x - 3

A: gx=3x+2x2-2x-3 The domain of given function is the set of all values of x for which denominator is…

Q: The function f(x) = 2x – 33x2 + 144x +7 has one local minimum and one local maximum. This function…

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Q: The function f(x) = -(x + 3)² - 4 has a vertex of (-3, -4).

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Q: The function f (x) = 5 + 6x + 96x 1 has one local minimum and one local maximum. - This function has…

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Q: Use the function f(x) =3x2-5x,g(x)=6x-4,h(x)=5-x3 find the (gof)(x)

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Q: Let f(x) = x2 - 5 and g(x) = 3x + 2. Find (f-g)(5).

A: As their are two different question, we have answered first question only and if you want solution…

Q: Sketch a graph of the function. 28- f(x) = -x3 + x2 + 8x – 12 24- Use the graphing tool to graph the…

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Q: inflection point if any of the function  g(x)=9x^3 - 4x

A: Inflection point of given function is (0, 0)

Q: The function f(x) – 2x° + 27x² – 84x + 4 has one local minimum and one local maximum. || This…

A: Maxima and Minima Question

Q: Find the domain of the function : g(x) = 1 /(x2 + 4) -1/(x2 - 4).

A: Given, gx=1x2+4-1x2-4

Q: Let f(x)= -4x+3 and g(x)=x^2 -2 Find (g-f)(x)=

A:

Q: Consider the function: g(x)= 6x+14|x|/5x-7|x| 1. (limxinf0^- )g(x)= 2. g(0)= 3.…

A: Given:

Q: Find a rule for g-(x) if: g(x)=4x

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Q: Find f(x) such that f'(x)=2x4 - 4x and f(2) = 3

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Q: Find the asympototes of f(x)= x4-2/x3+1

A: f(x)= x4-2/x3+1 We can find the vertical asymptotes by finding the values that make the function…

Q: Differentiate the function. g(x) = x 2 (1-2x)

A: Given:gx=x21-2xFormula:ddxxn=nxn-1

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.