Theorem: Let f,g € C(X)are continuous function then 1) f + g is continuous function and (f + g)(x) = f(x) + g(x) 2) f.g is continuous function and (f.g)(x) = f(x). g(x) 3) is continuous function and () (x) = g(x) # 0 f(x) g(x) g.

Q: If f and g are differentiable at a , then f (x) + 4g (x) = I (x) + g (x)]. True False

A: Here, the given statement is  If f and g are differentiable at a, then ddxf(x)+ddxg(x)=ddxf(x)+g(x)

Q: 3) Find Domain and Range of the function; 1 2x-5 f(x) =

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Q: I + 9 If f(x) = 7x – 9 and g(x) 7 (a) f(g(x)) = (b) g(f(x)) = (c) Thus g(x) is called an function of…

A: Given: f(x)=7x-9 and gx=x+97. a fgx=fx+97                 =7x+97-9          ( Put the value x+97  in…

Q: The functions f and g are defined as f(x) = 4x +3 and g(x) = 1-2x 91 and a) Find the domain of f, g,…

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Q: What is the domain of the function? f (x) = x-2 2x²+x-10 O (-∞, -/ ) U (-2,00) o (−o, −2) U(-2, 5)…

A: We have to find the domain of the function  f(x) = x-22x2+x-10.

Q: a+5 If f(z) = 3z-5 and g(z) = 3 %3D (a) f(g(z)) = (b) g(f(z)) = %3D (c) Thus g(z) is called an…

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Q: Find the values and expressions in parts a through h for the function f(x) = /x< +5x. (a) f(0) (b)…

A: Since you have asked multiple subpart,as per our guidelines we are supposed to answer only first 3…

Q: e*+1 Differentiate the function f(x)= In -3x +1 -3e A) 4e** +1 +1 3e B) e +1 +1 3e C) 3x 1. D) E) +1

A: Topic: differentiation

Q: Can you please find (f o g o h)(x) where f, g and h are defined, and it's in the attached picture.…

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Q: If function f(x) and g(x) are continuous everywhere then: * O (f/g)(x) is als continuous everywhere…

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Q: Prove that: g(x)Vf(x) – f(x)Vg(x) (@)V %3D g(x), a* + (a? + 1)²a** g(x)g(x – 1) | -对tre (b)A² %3D…

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Q: Let f(x) Determine a function 4 – x | y = g(x) so that f(g(x)) x + 3

A: Given f(x)=x+14-x

Q: If f(x) = x + 3 and g(x) = - 3, (a) f(g(x)) %3D (b) g(f(x)) = %3D (c) Thus g(x) is called an…

A: f(x)=x+3,g(x)=x-3

Q: What is true about the function f(x)= = a) f(x) → from above b) f(x) →2 from above c) f(x) → from…

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Q: Consider the function y = (x) where f(x) = x³ +2x2 - 4x and g(x) = x2 + 2. Determine a) the domain…

A: The domain of definition of a function is a set of those values for which we can define a function.…

Q: find (f+g)(x) (f-g)(x) (f•g)(x) (f/g)(x) and their domains

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Q: If f(x) = x + 7 and g(x) = x - 7, (a) f(g(x)) (b) g(f(x)) = (c) Thus g(x) is called an - Question…

A: given f(x)=x+7 and g(x)=x-7

Q: If f(x) = z + 5 and g(z) = z - 5, (a) f(9(x)) (b) 9(f(x)) (c) Thus g(z) is called an function of…

A: Given f(x)=x+5 and g(x)=x-5. a. f(g(x)) As g(x)=x-5 we will substitute the value in place of g(x)…

Q: he function f (x) is defined below. What is the end behavior of f(x)? f (x) = 8a® – 64x ³ – 640x? –…

A: Given query is to find the end behaviour of the polynomial.

Q: Suppose the point (-3, 10) lies on y = f(x) and the point (2, -3) lie point on the function y =…

A: Introduction: The function f(g(x)) or (f ∘g) represents the combination of functions f(x) and g(x),…

Q: 2 Identify f(x), g(x), and h(x) such that F(x) = f(g(h(x))) for the function F(x) = Vin(x+ In(x+ +…

A: We need to find f(x), g(x) and h(x) from F(x).

Q: If f(x) = x + 3 and g(x) = x – 3, (a) f(g(x)) : (b) g(f(x)) = (c) Thus g(x) is called an function of…

A: Since you have asked multiple questions in a single request, we would be answering only the first…