Determine the interval(s) over which f(x) = (x − 4)³ is concave downward. O a O b Od (-∞0, 4) (-∞, -4) (4,00) (-4, ∞0)

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A: Range :- set of all output values

Q: Use algebraic manipulation to prove that (X +Y)(X + Y) = X

A: Given: X+YX+Y=X Now, first we shall simplify left hand side of equation.

Q: The Range of the quadratic function f(x) = -x² + 15x + 45 is O (0,8] О -45, 8 O [-8, 0) O [45, 0) O…

A: By sketching the graph

Q: 12 - y = | 4-x | Which of the following is the value set of the function? A) (-∞, 0) B) (-∞, ∞)…

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Q: f(x) = 8+x 8 - x on [4, 6].

A:

Q: Let f(x) = 6x² + 2x³. Select all intervals where f(x) is INCREASING, (3) (0, ∞) (,0) (-∞, -3¹²¹)

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Q: Let f(x) = 5x-4 and g(x) = x2 - 1. Find (go f)(-1). O A. -82 о в. -4 о с. 0 O D. 80 O A О в O c O D

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Q: If f(z) = (a") + and f(z +y) + f(z-y) Kf(z)f(y), then the 21 value of K.

A: Given that: *f(x)=ax+a-x2 *f(x+y)+f(x-y)=K×f(x)×f(y) Thus, the function f(x+y) is,…

Q: x=[-5,-4,-3,-2,-1,0,1,2,3,4,5], A= [0.45    0.61    0.75    0.88    0.96   1    0.96    0.88    0.75…

A: Given: x=[-5,-4,-3,-2,-1,0,1,2,3,4,5], A= [0.45    0.61    0.75    0.88    0.96   1    0.96    0.88…

Q: The function below has the form f(x) = a · b² + k. %3D 14 Which of the following functions is shown…

A: Functions

Q: giver yn f(५) ५) -2x + 3, + 2, find of ax

A:

Q: What is the domain of the function f (x) : (-1,0) U [1, 00) b. (-1,0] U (1, ∞) c. (-00, –1) U [0,1)…

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Q: If f (x) = x² - x and g(x)=√x-2, what is (fog)(x) ? Simplify your answer. x²-x-2 /x² - 2 2-x-2 O…

A:

Q: fg)(x)=  f(x)=3x−8 and g(x)=x2+16x+63 Use “U” to indicate the union of intervals.

A:

Q: On which interval is the function f(x) = x2 - 2x - 8 decreasing? A [-2, 4] B (-∞, 4) C…

A: Given, f(x) = x2 - 2x - 8

Q: What are intervals of concavity of the function f(x) = -2x + 6x² – 3 ? a. Concave upward on (-1, o0)…

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Q: Find where f(x) = 1-ax x(x-a)(x+b) is discontinuous.

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Q: 2х f(x) = ,x 1

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Q: Find the polynomial f(x) for which x· f(x – 1) = (x – 3) · f(x), Væ |

A: find the polynomial f(x) for which  x fx-1=x-3 fx ∀x for x=0 x fx-1=x-3 fx ∀x

Q: On what interval(s) is the function f(x) = x99x8 + 5 both decreasing and concave up? (Enter your…

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Q: $42] B. (-∞0.42) C. (-∞,21] C

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Q: 4. please help!'   Calculate the domain of the function:

A: Step 1:

Q: (x+1)(x-2)². On what interval (2) (x - 5) let g"(x) = is g Concave up? (Note: you are given g" but…

A: g''x=x+1x-22x-5

Q: i Which of the following functions have zeros at 1 and -2? (x + 4)(x+2)(x = } x + 3){x – 4) I. f(x)…

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Q: differentiate f(x) = O O O O - 1 1 9x2+ 13x-5 18x + 13 (9x²+ 13x - 5) 3/2 1 (9x² + 13x - 5) 3/2 18x…

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Q: Express the function in the form fog. (i) F(x) = (2r + r*)ª. (ii) F(r) = %3D 1+ VE

A: Answer

Q: which of the following intervals the function f(x) = x² + 3x – 4 is increasing?

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Q: Linearization X = a [스 (b+y)

A: Linearization is done to obtain an equivalent linear equation for a given equation. The linear…

Q: Let f(x) Then (f o g)(x) — 5а — 4 and д(x) — г* — 4+ 2. 4х + 2. = x - - (go f)(x)

A: