60. A composition of functions is ... A) is adding two or more functions together. B) using the results of one function to evaluate a second function. C) taking a function and rewriting it as two separate functions. D) anytime a function is written down. 61. The notation (f o g)(x) is equivalent to ... A) f(x) •g(x) B) (fg)(x) C) f[g(x)] D) g[f(x)]

Q: 3) Show that (f o g)(x) = (go f)(x) = x. f (x) = 4 – 3x g(x) = (4 – x)

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Q: [6] Use the algebraic test to determine if these functions are odd, even, or neither. [Odd: f(-x) =…

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Q: (a) Let n and k be non-negative integers. Explain what the function pr(n) counts.

A: Since you have asked multiple questions, we will solve first one. If you want solved other question,…

Q: 10. If the domain of f(x) is (–∞0,6] and the domain of g(x) is (–9,00), then what is the domain of…

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Q: 4. Suppose P is the set of people alive today and C is the setof possible eye colors. Let f : P → C…

A: Given :          P is the set of people alive today and C is the set of possible eye colors.…

Q: Question number 2.

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Q: - Find and classify the discontinuities of the function f(x) x2 - 1

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Q: What must be true about the integer n if the function f(x) = x^ n is an even function? If it is an…

A: Given that,

Q: Suppose f is a function satisfying f(-9) = 5 and f'(-8.98) = . Use this information to approximate…

A: SOLUTION-

Q: 3. Determine whether the statement is true of false. If it is false, give an example that shows it…

A: Given: f'(x)=g'(x) So, we can write as: dfxdx=dgxdxdfx=dgx...Integrate on both…

Q: 6) Determine whether the following function is one-to-one. f(x) = {(3,6), (-2,5), (4, –2), (-4, 6),…

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Q: 24 Find the function that corresponds to the graph below. -5 f(x) = 1 · 4* O f(x) = 2· 4* f(x) = 1 ·…

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Q: Let k(x)=f(x)g(x)h(x). If f(−2)=−5,f′(−2)=9,g(−2)=−7,g′(−2)=8,h(−2)=3, and h′(−2)=−10 what is…

A:

Q: Suppose that f  has domain A and  g has domain B .(a) What is the domain of  f+g?(b) What is the…

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Q: 58. Given that the domain of a one-to-one function f is [-3, 5) and the range of f is (-2, ∞), state…

A: Given, the domain of a function f is [-3,5) and range of is (-2,∞)

Q: 4. If F(x) = f(xf (xf(x))), determine F'(1) when f(1) = 2, ƒ (2) = 3, f'(1) = 4, f'(2) = 5, f'(3) =…

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Q: 22 – 1 Are functions f(x) and g(x) = x - 1 the same? Why? Explain in a full sentences. x +1

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Q: Let k(x)=f(x)g(x)h(x). If f(5)=−9,f′(5)=0,g(5)=−3, g′(5)=9,h(5)=−8, and h′(5)=−4, what is k′(5)?

A: Given, k(x)=f(x)g(x)h(x). If f(5)=−9,f′(5)=0,g(5)=−3, g′(5)=9,h(5)=−8and h′(5)=−4

Q: State the restrictions on the domain of the function. (* +7)(x- 9) f(2) = (x - 3)(x +7) O x # 3 or 9…

A: Given function is fx=x+7x−9x−3x+7. We have to state the restrictions on the domain of the function.…

Q: What describes a true relationship between the f(x) and g(x) over the interval [2,4] 4 f(x) 1 3 7 9.…

A: Follow step 2 .

Q: 8. A car manufacturer determines that its profit odeled by the function P(x) = 0.00125x4 + x - 3, wi…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 3. Let f : A → B. Then 1gf = f and f14 = f. Hint. You may use the fact that fg, for functions f, g,…

A: Let               f1 : X→Y , f2 : X→Y be two functions, then we say that the functions f1 and f2 are…

Q: 25 – 3 Evaluate the domain of the function h(z) = 3 - z2 - i

A: The domain of a complex function f(z), is the values of z for which the function is defined .

Q: 15. Evaluate the difference quotient f(x + h) – f(x) for h 3 f(x)

A: The difference quotient of a function f is given by, f(x+h)-f(x)h. To find f(x+h) replac, x by x+h…

Q: Prove or disprove. The function f(2) = 2z – 3 – ze? + e=% is not entire.

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Q: 11. What property must f(x) have in order for f'(x) to exist?

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Q: 58. Show that if f is a function and z = x+h, then f(2) – f(x) _ f(x+ h) – f(x) Z - x h

A: This question is taken from the function in which we have to prove the given equation. We can write…

Q: 7. Given the sketch of f(x), create the sketch for f'(x) fAx)

A: We have to sketch the graph of the function f'x. First we have to find the function of the given…

Q: 1. Determine and completely simplify f(x + h) – f(x) for f(x) = -7 Зх + 1

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Q: 10.Let f(x) = – x² -x – 6 and g(x) = 2x + 6, find f(g(x))

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Q: 6. Below is an injective function. * A 3 C D O A. True O B. False 2.

A: See the details solution in below

Q: 11. Which graph represents the function f(x)=2sin⁡(3θ)?

A: The solution is :

Q: 8. Which statement best describes the end behavior of the function f(x) = 3 – 5z +2x2-72°? O f(2)…

A: End Behaviour of function.

Q: 19. If the original function Ax) = 2x² – 1 is shifted to the left 3 units to make the function g(x),…

A: Solve the following

Q: function f(x)=4x^5? A- the function is even becuase f(-x)=f(x) B- the function is odd because…

A: I am attaching image so that you understand each and every step.

Q: 18. Use the vertical line test to determine if y is a function of x in the graph. Which of the…

A: The given problem is to check the given figure is the function of x or not using the vertical lines…

Q: What is the domain of the function f (x) = -4|a + 1-3? O (00,00) O (1,-3) O (-00,-3] O (0,00)

A: We have to find the domain of the function  f(x) = -4|x + 1| - 3

Q: x² – 4 Ax) xx – 2

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Q: 2. Fillin the table below forthe functionゾ(x)-2x3-1 and explain whether f(x) is even, odd, or…

A: To check whether the given function with respect to the given requirements

Q: ) = , 1 as x → 3+? What is true about this function f( x x2 -9 O f(x) O f(x) → 0 from below O f(x) →…

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Q: =8. If f(x) and g(x) = x2-4, then what is f(g(-2))? x+ 4

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Q: das Similarly, evaluate f(x) for the values below, and complete the table. 3.5 3 2.5 2 1.5 f(x) 1.75…

A: In question we need to find f(x) and complete the table.

Q: What is the correspondence of f(x) = 3x - 6

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Q: 11 , find the composition fog and simplify your answer as much as possible. Write the domain using…

A: Fog(x)=f(g(x)=f(11/x)

Q: Suppose that f(x) and g(x) are functions with f '(2) = 5 and g'(2) = 3. Let h(x) =f(x) + 2g(x). What…

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Q: 33) Use the numerical representation of f(x) below to give a numerical representation of g(x)-f(2x)…

A: To evaluate g(x) at various points using the definition in terms of f(x)

Q: Consider the piecewise function f(x) defined by 6 2x if x 4 or which x E R is f(x) continuous? You…

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Q: Let h(x)=f(x)/g(x), where f(−3)=7,f′(−3)=−9,g(−3)=−2, and g′(−3)=1. What is h′(−3)?

A: Given query is to find indicated derivative.

Q: 5a.

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Q: 2. Suppose that f(x) is a function with f(20) = 345 and f'(20)=6. Estimate f(22). [4 marks]

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