Consider the values of f and g in the given table. f'(x) g(x) g'(x) 3 4 -3 -2 -1 -2 3 2 -4 -1 0 -3 1 2 3 4 f(x) 2 1 3 -1 Compute: f(g(x))₂-1 d dx Compute: g(f(x)),-1 d dx d Compute: f(x³ - x²) |z=2 dx Compute: (g(x)³ - g(x)²) |__2 d · dr.

Q: b) Find f(")(x) is f(x) =

A: The derived function is a function f  where f'(x) is the derivative of f at x, is the derived…

Q: Find the function f (x) for which f (x) = e-5x, f (0) = 1.

A: A function is a relation which maps each value in its domain to exactly one value in its range. For…

Q: Consider the function y = (a) Find the x- and y-intercepts of f(x)

A: An x-intercept of a function f(x) is a point on the x-axis at which the graph of the function f(x)…

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Q: Use the given graph of y = f(x) to graph the function g : g(x) = f(x + 1) + 1

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Q: Find f′(x) and f′(c). Function f(x) = (x − 4)/(x + 4) Value of c = 3

A: Now differentiating with respect to x, we get

Q: The linearization of f (x) = x² based at 3 is L (x) = [ Select ] [ Select ] (x - [ Select ] Done […

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Q: Let f(x) = 3x- 4 and let g(x)= 2x+1. Find the given value. flg(1)] flg(1)] = (Type an integer or a…

A: SOL : → g(x) = 2x+1 .           ⇒ g(1) = 2×1 + 1                         = 3

Q: Is the two functions h(t) and g(t), is h-1g-1 (t) = (hg)-1(t)

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Q: X x + 2 A1. The functions f and g are defined by f(x) (a) Calculate f'(x) and g'(x). d (b) Calculate…

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Q: 3. Find f(x) and f (x) if f(x) = lnx + 2cos³ x. %3D

A: First use sum/difference rule of differentiation f±g=f'±g' then use the following formulae: dln…

Q: Of (x) = (4x-6x* + 4 3 3 Of (x) = x* – 2x³ + 5 Of (x) = x* – x³ +4 6 ,3 %3D f (r) – 2r4 6r3 1 8

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Q: f (1), where f (x) = 21 + x2

A: Given function - f(x) = x2+21         ...........(1)f-11 = ?First we need to find the inverse…

Q: Find the local extrema points of the function f(x)=(x−a)ex, where a is an arbitrary real number.

A: Consider the function

Q: Use the table to determine Df(g(x))) at x = 3. |1 2 3 4 f(x) 1 f(x) |3 -5 1 4 4 1 3 4 3 2 g(x) 2…

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Q: Find  f (n)(x).   f(x)  = 2x

A: Given that f(x)=2x

Q: Find f ′(x) for the function f (x) = 7x −8

A: Differentiation is the process of finding derivative or rate of change of a function. Suppose we…

Q: Let f(x) and g(x) be defined as follows: f(x) = 2x+ 1, g(x) = /x-3 What is (fog)(x)?

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Q: Find f′′(x). f(x)=(x 2+2)9

A: Given fx=x2+29. The objective is to find f"x.

Q: 1. Use forward and backward difference approximations of O(h) and a centered difference…

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Q: For the function f(z) 2(x – 5) + 7, which of these equations describes f '(r), the inverse of the…

A: We wil use concept of inverse function to find the answer.

Q: Consider the following. f(x) = 8x - 3, g(x) = 1 - x The quotient of two functions, (f/g)(x), is…

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Q: f(x)=xnex

A: f(x)=xn exThe doamin of the function is when n is even and odd is x∈ℝand the range of the function…

Q: 3. Let f(x) = x¹/3 and g(x) = 2x² + 5x – 1. A. Write out the equations for all four functions: ƒ(x),…

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Q: Consider the function g(x)=(f(x))^5. If f(4)=3 and f′(4)=−2, then find g′(4).

A: Given: g(x)=f(x)5f(4)=3f'(4)=-2

Q: F(x) = 2ln(x). What is F′(2)?

A: we have to find derivative of f(x) at x=2where f(x) is given by

Q: 2. (a) (5 points) Let f(x) = Vr +1 and g(x) = x² + 2x. Find (f o g)(1) and (go f)(1). %3D %3D 1+ x…

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Q: Find (ho g)(x) for the indicated functions. h(x) = Vx+4, g(x) = x+3 (ho g)(x) =D

A: Given,          hx=x+4 , gx=5x+3