The composition (f g)(x) is defined for all values of x for which x is in the domain of, and g(x) is in the domain of.

Q: State the domain of f g. Then find f• g, including any additional restrictions necessary on the…

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Q: The function (f/g)(x) is defined for all values of x that are in the domain(s) of  both f and g, and…

A: The denominator can not be equal to 0  Because any constant divided by 0 is undefined

Q: 16. Let f(x) = -x³ + 3x - 4 and g(x) = 2 – x. Find the composition (f(g)) and its domain. Rep the…

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: Let alpha be a zero of f(x) =x2 + 2x +2 in some extension field of Z3. Find the other zero of f(x)…

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Q: Let f(x) - x2 - 5 and g(x) - 7 - x. Find a formula for h(x) - f(g(x)) + g(f(x)) in terms of x. h(x)…

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Q: Define g(-5) in a way that extends g(x)= 9(-5) = x² - 25 x + 8x + 15 to be continuous at x = -5.

A: We have to define g(-5) such that g(x) is continuous at x = -5.

Q: 2. Let R be a U.F.D. and f (x), g (x) e R [x]. If f(x) g (x) is a primitive polynomial, then f (x)…

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Q: (8 •h)(x) %3D

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Q: 2 For the real-valued functions f (x)=x´- 3 and g (x)= /x-4, find the compositionƒ °g and specify…

A: Given f(x)=x2-3 g(x)=x-4

Q: he domain of the composition: For f(x)=2x-5 and g(x)=√x+7, what is the domain of g of? terval…

A: Given query is to find the domain of the composite function.

Q: Let f (x) = x>(x2 - 1), g(x) = (1 - x)>(1 + x), and h(x) = 2>(3x + 1). Express as rational…

A: fx=xx2-1,  gx=1-x1+x  &  hx=23x+1 Now, gx+1=1-x+11+x+1=1-x-1x+2=-xx+2

Q: Let k(x) f(x)g(x) h(x) If f (x) = 3x, g(x) = x - 2, and h(x) = -x² + x + 1, what is k' (x)? %3D…

A: We know that, from quotient rule of differentiation We have,  fx=3x, gx=x-2 and hx=-x2+x+1 Now,…

Q: Let g(x) =−x2 +4x+1−x2 +4x+1 Find when:   g(2), and  g(t)

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Q: Suppose that f(x)=A/x,     g(x)=Bx^3, and    h(x)=ax^2+bx+c   Assume A≠0. Compute the composition…

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Q: 1 Let f(x): and g(x) = x2 – 6x. x + 8 Find the domain of the composition (fog)(x)using set notation.…

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Q: For the real-valued functions g (x)= x+2 and h (x) =2x+1, find the composition g °h and specify its…

A: The domain of a function y=f(x) is the set of all possible values of x for which f(x) is defined.

Q: The function g is defined by g(x) x € R, x+ In 2 (a) Differentiate g(x) to show that g'(x)=- (e* –…

A: We use Quotient rule

Q: find the largest domain for f(x) = (x-3)2   with an upper x bound of 8 such that the function f is…

A: fx=x-32 Differentiating with respect to x, we get f'x=2x-3 Now function is non decreasing in the…

Q: For the real-valued functions g(x): = notation. (8 h)(x) = 0 Domain of g h : 0 x-4 and h(x) = 4x+7,…

A: Given, g(x)=(x-4)/(x+1) h(x)=4x+7

Q: Let f(x) = 3x -2 and let g(x) = 5x + 5. Find f(x) - g(x). %3D %3D Type the coefficients in the…

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Q: For y = In (x' + 3x - 9) , to find would require the chain rule. If y = f(g(x)) find an f(x) and…

A: Given that        y = ln(x7+3x-9)

Q: Consider a polynomial f(x) with real coefficients having the property f(g(x)) = g( f(x)) for every…

A: The property is fgx=gfx. If f(x) is x2+2x+1, find the inverse and assume it as g(x).…

Q: Prove that f(x) = (x- 1)2 + (x + 1)? is an even function. A function k(x) is an even function if…

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Q: The polynomial function f ( x ) = x 4 − 19 x 3 + 134 x 2 − 414 x + 468 has 5 + i as a zero. Select…

A: Given that f(x)=x4-19x3+134x2-414x+468 has one zero at x=5+i. We need to find the other 3 zeros.

Q: f(x)g(x) - f(c)g(c) = f(x)(g(x) - g(c)) + g(c)(f(x) - f(c )). Prove the product rule

A: In this question we will use basic of calculus i.e concept of differentiability. Solution of the…

Q: 4. Let f (g(x)) = (3x – 5)² + 1 and g(f(x)) = 3x² – 2. Find a single formula for f and a single…

A: We have given that f(g(x))=3x-52+1 and g(f(x))=3x2-2. We have to find for single formula for f and a…

Q: Let f(x) = 5x4 + 3x3 + 1 and g(x) =3x2 + 2x + 1 in Z7[x].  Determine the quotient and the remainder…

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Q: 1- prove that if y=f(x) is continuous and f(x)=0 when  x is a rational number, then f(x)=0 for all…

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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: Let ƒ(x) = x - 3, g(x) = √x, h(x) = x3, and j(x) = 2x. Expresseach of the functions as a composition…

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Q: (d) Let k(x) = h(g(x)). Find all values of x such that k'(x) 2

A: Here we use derivative of composition.

Q: Define g(4) in a way that extends g(x) = (x2 - 16)/(x2 - 3x - 4) to be continuous at x = 4.

A: On simplification, we get

Q: Let f(x) = 2x - 5 g(x) = 4x – 1 h(x) = x² + x + 2 Evaluate. (g of)(0) O-21 O -7

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Q: assume f(g(x))=x and f'(x)=1+f2(x) for all x. show that g'(x)=1/(1+x2)

A: Differentiate both sides of f(g(x))=x with respect to x. Use chain rule on the left side.

Q: et f(x) = 4x + 2 and g(x) = 2x2-4. Find the formula for the composition function gf.

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Q: Let f(x) is defined as (kx² – 1, S (x) = x-1 Determine k so that the fur

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Q: (a) A function f(x) is defined by 3x + 4; x 2 1 -5 x+6B f(x) = -5 -3x – 4; Discuss the continuity…

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Q: 3. For f(x) = x' + 14, find all x such that f(x) = -13.

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Q: 5. Given f(x)=Vx+4 and g(x)= x² -5, find (f•g)(x) and (g o f)(x) and the domain of each composition.

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Q: A(n) function f is one for which f(- x2) = f(x) for every x in the domain of f; a(n)  __________…

A: A(n) function f is one for which f-x=fx for every x in the domain of f; a(n)  __________ function f…

Q: Let f be the function Зх + 5 for x 5 х Compute the left- and right-hand limits at x = 5 and…

A: Now, Left hand limit at x = 5 is, And right hand limit is,

Q: which are polynomial functions f(x)=4^x  -1 g(x)=7x^4  -10x^2  -9 h(x)=tanx

A: Hi, Thank you for the question. Since you have posted a question with multiple sub parts, as per the…

Q: 3x + 7x2-5x-4 Let f(x) = %3D 6x +4 1. Use Ad-hoc calculations to prove that f(x) is O(x2) 2. Use…

A: let fx=3x3+7x2-5x-46x+4 1) use the Ad-hoc calculations to prove that fx is Ox2 2) use limits to…

Q: For f(x)=2x3+4x2+3x-7, prove that there exist a number k such that f(k)=20.

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Q: Let ƒ(x) = x - 3, g(x) = √x, h(x) = x3, and j(x) = 2x. Expresseach of the functions as a composition…

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Q: Givenf (x) = for x # 3; ƒ-l (x) = ? x - 3 Of-1 (x) = 3+2 x-1 Of-l (x) = 3x+2 x-1 X- f-' (x) = 2 x+1…

A: Steps Rewrite f(x) as y Swap x and y Solve of y.

Q: Let f(x) = V1 – x and g(x) = . Determine the following composition and its domain. gof

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Q: Let h(x) = x - 4 and g(x) = x2 + 2x

A: The composite function f(g(x)) is known as function f of function g. It is obtained by substituting…

Q: Define g(3) in a way that extends g(x) = (x2 - 9)/(x - 3) to be continuous at x = 3.

A: Here, the given function The function gx is continuous at  x=a, if the following holds: (i) ga is…

Q: Suppose that f(x) and g(x) are polynomials in x . Can the graph of f(x)/g(x) have an asymptote if…

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