Consider the following function. (4x + 1, 1x² - 4₁ (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) -1,2 f(x) = increasing (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) (-∞, -1),(0,00) (-1,0) decreasing X x < -1 x>-1 relative minimum (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) relative maximum (x, y) = -1, 3 (x, y) = DNE X

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A: Given:  fx=3-x,    gx=x2-1   To find:  a) f+gb) f-gc) fgd) fg And their corresponding domains.

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A: Which option represents  the amount of water in the second bucket.

Q: Where does the graph of the function h (x) = x* + 3z² – 4 cross the x-axis? %3D O x= -1 and x = 1 O…

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

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Q: Find the interval where the function, 3 f(x) = * - 4x – 2x? is increasing? O a. (-2,-1) O b. (-∞,…

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Q: ider the ns. f(x) = x2, g(x) = x + 8 Find (fo g)(x). Find the domain of (fo g)(x). (Enter your…

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Q: Find the interval where the function, -x2 f(x) = - x + 2 is increasing? | a. (-o, –1) O b. (-2, -1)…

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Q: Refer to the functions f and g and evaluate the functions at x =-2. f = {(2, -1), (1, 1), (-4, -6),…

A: (f+g)(-2)=f(-2)+g(-2)  Substitute   f(-2)=-8  ,    g(-2)=-5in the above equation

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A: given , the functionfx=x36-x24i)Dinomination cant be…

Q: Find each of the following functions. f(x) = V3 – x, g(x) = V x2 – 4 (a) f+ g State the domain of…

A: Domain of a function: The domain of a function is the set of all possible input values. The given…