Given the following functions, compute the composition (f • g)(x). f(x) = -3x² – 4x + 2 g(x) = 2x – 1 Simplify your answer and collect like terms. Do not include "f(g(x)) =" in your answer.

Q: Suppose that f(x) = 11e^(x) - ex^(e). Find f'(3).

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

A: We need to express the above function h(x) as a composition of two functions f(x) and g(x) such…

Q: Suppose ƒ is an even function and Evaluate

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Q: Find the domain of function defined as follows. y = ln(x2 - 16)

A: y=lnx2-16Domain:       The domain of a function is the set of all possibleinputs for the function

Q: Find a general formula for f (n)(x). f (x) = xe−x

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Q: (;) 9 and () ). For the functions f (x) = 4x4 – 19x³ – 10x2 + 35x – 50 and g(x) = x – 5, find E) (x)…

A: Consider the provided functions, fx=4x4-19x3-10x2+35x-50    and    gx=x-5 Find the value of fgx…

Q: Given the following functions, compute the composition (fog)(x). f(x) = 8x + 4 g(x) = 2x-6

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Q: 23. f(x)=7* + 4e*

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Q: 4.Find f (1) for f(x) = x² + 5x + 2

A: Given: f(x) = x2+5x+2.

Q: Given f(x)=9x^2−7x+4, find f'(x) using the limit definition of the derivative. f'(x)= If you dont…

A: Given function, fx=9x2-7x+4

Q: ) Find the values of the constant a so that the function f (x) will be continuous for all x. fax +…

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Q: Find f'(0) for f(x) x = 0. 0,

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Q: 2. If f(x) = 1 + x², find fof 3.lf f(x) = -x, g(x) = 2x + 1 and h(x) = x², find fogoh,

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Q: ,if x>2 Find the correct value of bb that makes

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Q: 2.) For the functions f (x) = 3x + 5 and g(x) = 2x – 8 find (E) (x) and give its domain in interval…

A: Consider the functions  f(x)=3x+5g(x)=2x−8

Q: For the following pairs of functions, determine which function grows faster. f(x) = 6x – 5a² + 9,…

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Q: Find the value of k so that the function 5x+3 if x<3 f(x) =. kx2 if x 23 is continuous everywhere?

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Q: Find the quotient and the remainder upon dividing f(x) = 2x°+4x*+3x+1 by g(x) = 3x+1 in Z„[X].

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Q: Let g(x) x2+4. Find a function f that produces the given composition (fo g(x)= x+8x2+27

A: (fog)(x) means f(g(x)). Plug g(x)=x^2+4.

Q: 10. For f(x) = -x² +5, find f(a+h)– f(a) if h+0.

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Q: For this function Y=x^3 + 15x^2 -225x prove that we have a point of inflection at x=-5

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Q: Find a general formula for f (n)(x). f (x) = x−1/2

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Q: Give the formula for f(n) (x) where f(x)= 1/(3x-1)

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Q: 4.) For the functions f (x) = V16 – x and g(x) = 2x – 8 find (f • g)(x) and give its domain in…

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Q: 6 Given the function f (a) = , find f'(1). Express your answer as a - single fraction in simplest…

A: This question is related to differentiation, We will solve it using given information.

Q: Suppose you have just finished approximating f (x) = x3 for 0 ≤ x ≤ α and ended up with φˆ(α, x) =…

A: Given suppose you have just finished approximation f(x) =x3 for 0≤x≤α and ended up with φ^ α, x=…

Q: Find the inverse 0f             y =f(x)= x2, if x ≥ 0. Graph f and f -1.

A: A function g is the inverse of function f if for y=fx,  x=gy Inverse of x2:y=x2Replace x and…

Q: Given h(x) = 5x + 8 and f(x) =1/2x + 2, evaluate the composite function. f[h(0)]

A: The given functions are,

Q: Given f(x): 5x² 6x +13, find f'(x) using the limit definition of the derivative. f'(x)=

A: Given problem:- Given f(x)= = 5x²-6x+13, find f'(x) using the limit definition of the derivative.

Q: Make the composition (f o g) (x) with the function f (x) = x ^ 2 + 2 -2 and g (x) = √x

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Q: Help 1

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Q: Proceed as in Exercise 51 to calculate F'(0), where 3x + 5x* + 5x +1 F(x) = (1+x +x*/3 +x/³) : 8x9 –…

A: Given function is Fx=1+x+x43+x533x5+5x4+5x+18x9-7x4+1. First multiply the numerator.…

Q: Next, differentiate the given function y = X 8x + 37 and write as a single fraction completely…

A: Derivative of function

Q: Find the value for k so that the function will be continuous at x = 2. 4x + 16 if x 2

A: The function fx is continuous at x=a, if limx→a-fx=limx→a+fx It is given that fx=4x+16if…

Q: 2. If f"(x) = 4sinx+16cosx, f(0) = 6, f'(0) = 1, find f(x) and f(4).

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Q: Find f' (æ) for f (x) = 7 ln(4 + æ²).

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Q: 5. For the functions f (x) x²+1 and g(x) = Vx +2 , simplify the composition x²-2 f (g(x)) and state…

A: We are solving the first question and for the next question post the question again and also mention…

Q: For the real-valued functions f (x)3D2x-1 and g (x) =Vx-4, find the composition f og and s

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Q: Given h(x) = 7x + 8 and f(x) = 1/4 x + 7,  evaluate the composite function.   f[h(0)]

A: Given:

Q: Suppose that f(x) 16e" – exº. Find f'(3). f'(3) =

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Q: Given f(x)=ln(5x), what is f'(x) when x=14.2?

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Q: For the given functions f and g , find the indicated composition. g(x) = 2x - 5 f(x) = 4x + 2x + 8,…

A: Given that,

Q: 8. For the function f(x)=3x+5-11, find the values of x such that f(x)=0.

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Q: I noticed that the difference quotient is always zero if f(x) = c, where c is any constant.

A: Difference quotient is also known as definition of limit. f'x=limh→0fx+h-fxh Given function is fx=c,…

Q: Find the requested composition functions.  given f(x)=4x^2+3x+6 and g(x)=3x-4, find (gof)(x)

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Q: For the function f(x) = (E)', find f-'(x). 8 Of (x) = (8/") || 4 Of (x) = (V8x)* f1 (x) = V (8æ)“…

A: Solution: The objective is to find the inverse of the given function

Q: 1. Use f(x) = x' - x' +x and g(x) = 2f(x+1)+3 to do the following:

A: Average Rate of change :The Average rate of change of function 'g' over the interval a≤x≤b is given…

Q: Suppose ƒ is an even function and Evaluate

A: Given f is an even function, ∫-88f(x)dx=18

Q: 10. For f(x) = -x² +5, find f(a+h)– f(a) if h +0. h

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Q: -3x Find f (x) given that f'(x)=x' +2-e* at (0,-1).

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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.