Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers for which f(x) is a real number. x -3 f(x) -5 f'(x) -1 0 4 2 3 1 -2 6 7 4 The table above gives values of a twice-differentiable function f and its first derivative f' for selected values of a . Let g be the function defined by g(x) = f(x² - x). It is known that g" (0) = -1. What is the value of f" (0) ?

Q: The graph of the derivative of f is shown below: -y-5 4 -3 -2- -1- 0 1 2 f'(x) 3 4 f', the…

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A: We will check the one to one of these functions

Q: 39,

A: Step 1:To show that the function f(x)=6x−2 defines a one-to-one (injective) function, we need to…

Q: Suppose that f is a function given as f(x) = -3x² - 2x - 3. Simplify the expression f(x + h). f(x +…

A: f(x)=-3x2-2x-3(i) f(x+h)=-3(x+h)2-2(x+h)-3

Q: #4. Determine the following attributes of f(x)= log,(3x+1)+2. a) `Find the x-intercept(s) of fx).…

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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: Consider the following functions: f(x)= x2+3 and g(x) = (1)/(x-4)   1) Find f (g(x)) . You are not…

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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: A function f has the form f(x) = Aekx. Find f if it is known that f(0) = 140 and f(1) = 266. (Hint:…

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Q: The one-to-one functions g and h are defined as follows. g(x) = -9x-2 h={(-2, 9), (0, 4), (3, 5),…

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