Suppose f and g are the piecewise-defined functions defined here. For each combination of functions in Exercises 51–56, (a) find its values at x = -1, x = 0, x = 1, x = 2, and x = 3, (b) sketch its graph, and (c) write the combination as a piecewise-defined function. f(x) = { (2x + 1, ifx < 0 x2, if x > 0 g(x) = { -x, if x < 2 5, if x > 2 8(4): 51. (f+g)(x) 52. 3f(x) 53. (gof)(x) 56. g(3x) 54. f(x) – 1 55. f(x – 1)

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Q: Let f(x) = 3x + 1, x, = -1, x, = 0, x3 = 1, x4 = 2, and X5 = 3. Find E f(x,).

A: we have the given the following details   f(x)=3x+1x1=-1x2=0x3=1x4=2x5=3We have to find∑i=15f(xi)

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Q: Discuss the continuity of the composite function h(x) = f(g(x)).

A: Given  The  functions are f(x)=5x+1  and  g(x)=x3 .

Q: 17. Let f be the function defined by f(x) x- 2

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Q: The function h is defined below. h(x) = -2x + 2 Find h(-2).

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Q: 6- Do a complete analysis to sketch the following function. F(x)=2x-x²/x²-2x+1

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Q: In Exercises 53-58, evaluate each piecewise function at the given values of the independent…

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Q: 3 Sketch a graph of the function f(x) = ax(x + 3)°(x – 1) , for some positive constant a. -

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Q: Assume that for a function f(x), f'(x) « O on the interval (-0, -5) and f'(x) » O on the interval…

A: From the given definition:  f ' (x) &lt; 0 when x &lt; -5 so graph must be decreasing in this…

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A: Introduction :

Q: Show that the GHASH function calculates (X1 • H™) Ð (X, · H"-1) © O (Xm-1° H²) O (Xm· H) ...

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Q: A function for which f(x) = f( - x) for all x in the domain of f is called a(n) ____function.

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Q: Discuss the continuity of the composite function h(x) = f(g(x)).

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Q: State the Mean-value Theorem, and use it to prove that a) if f(x) is differentiable and f'(x) > 0…

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Q: Express the function h(x) = (3x - 1)4 as a composition of two functions f and g so that h(x) = (f ∘…

A: Given: h(x) = (3x - 1)4

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Q: Show that the functions in Exercises 21-28 have exactly one zero in the given interval. 21. f(x) =…

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Q: Let f(x)=(x-3)/(x2-1).  What can you say about the long-term behavior of f?

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Q: Sketch a possible graph of a function that satisfies all of the following conditions: f'(2) = 0,…

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Q: Discuss the continuity of the composite function h(x) = f(g(x)).                                f(x)…

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Q: Find the constant a such that the function is continuous on the entire real number line. (x) = {x +…

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Q: Which of the functions graphed in Exercises 1-6 are one-to-one, and which are not? 1. 2. y =- 3x y…

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Q: b. Suppose the function h is defined as h(x) = 3f(x). Determine the domain and range of h.

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Q: A periodic function f(x) is defined as 3, f(x) = {x, f(x+2) -1≤x<0, 0≤x<1. Based on the above…

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Q: Find the domain of the below function: g(x)=In(x-x²)

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Q: The graph of the second derivative, f"(x), is given. > 10 6 -1 -2 -4 -6 -8 -101 Determine the…

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Q: x²+4 Let: f(x)= - 16x f'(x) = - f"(x)= 16(3x2+4) x² –4° (x²–4)² ' (x² –4)° 5. Sketch the graph of f,…

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Q: Let h(x)=f(x)g(x). If f(x)=x^2+4x−1,g(−2)=3, and g′(−2)=−5, what is h′(−2)?

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