77. If f is an odd function and g is an even function, show that the composite functions f°g and gof are both even.

Q: $6. Determine the complementary function for the given DE.

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Q: Use the following graph of f(x) to describe the behavior of f '(x). State where f '(x) is positive,…

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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: Suppose that a particular function f satisfies f" (x) = 12x? + 6x + 8, ƒ(0) = 1, f' (0) = –1. Then…

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Q: Suppose that f is an even function and g is an odd function (both with domain R) . If f(3)=4 and…

A: Given, f is an even function and g is an odd function. f(3)=4 and g(-3)=5 Identity: For even and odd…

Q: 1 65. Is the function given by G(x) = continuous бх + 8 at x = 2? Why or why not? 2.

A: To check the function G(x) = 1x2-6x+8 continuous at x = 2. G(x) = 1x2-6x+8

Q: Which of the following is the domain set of the function f (x,y)=arccos( x² +y -3)+ In(x² +y² -3) ?…

A: Domain of a function: The domain of a function fx is defined as the set of all values of x such that…

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…

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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: 13- Given that f(x) is an odd function, classify each of the following as even, odd, or neither .(…

A: The definition of even function is if f(-x)=f(x) and the odd function is f(-x)=-f(x) the odd…

Q: 11. Determine if the function 8(x)=,* 1 1 x²+x is either even, odd, or 4. neither (even nor odd).…

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Q: Give a possible formula for the function. f(8) = tan (x) Edit -Im-

A: The given graph shows the graph of tan(x):

Q: 67. If F(x) =f(g(x)), where f(-2) = 8, f'(-2) = 4, f'(5) = 3, g(5) = -2, and g'(5) = 6, find F'(5).…

A: F(x) = f(g(x))   x | f (x) | f ' (x) | g (x) | g ' (x) -------------------------------------- -2 | 8…

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: Use the function to find the absolute minimum and maximum and the local minimum and maximum.

A: At x=5 , y value is lowest. (y=2)So this is the absolute minimum.

Q: Find the avéragé raté of chanģė óf the function between the ĝiven valueš of x. y = -5x – x² between…

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Q: 10) Suppose that the functions f and g are defined as follows. fx) = -5x² + 2x g(x) = 3x – 2 Find()…

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

Q: Complete the statements for the function provided. f (x) = tan x Part 1 of 2 As x + 2 - S(x) - -00…

A: The objective is to solve the above question.

Q: Determine F(x) if, for all real x and y, F(x)F(y) – F(xy) = x + y.   Hint:  What could F(1) be?

A: Consider the provided question, We have to find F(x).

Q: Suppose, we want to define functions from set Ato set B Given that, B = n = 20 > 15 = m =HAw many…

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

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Q: Suppose g  is an odd function and let h=fog . Is h alwaysan odd function? What if f is odd? What if…

A: We know that a function is an odd function, if F(-x) =-F(x) and is an even function if F(-x)=F(x).…

Q: The domain of the function f(x)= tanh( x - 10) is Select one: O[-10, 10] O(0, ) None OR-{10} O [ 10,…

A: Set of values of x for which function is well defined is called domain of the function

Q: Use the given graph of f to find a number 8 such that if 0 < |x – 3| < 8 then If(x) – 2| < 0.5. - -…

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

A: The solution is :

Q: 3) Show that f = f, ху for the following function: ху (x° у) f(x. y) + In(x° + y30 ) 20

A: We have to prove that fxy = fyx

Q: 1. Determine the following using the graph of the functions / and & provided below. If the value is…

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Q: The domain of the function f(x)= tanh( x- 6) is Select one: O[6, *) O[-6.6] O(0, *) OR O None OR-(6)

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Q: Suppose f: Q+ → Z+ is defined by = mn for all positive integers m and n. Indicate whether f is a…

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Q: How many one-to-one functions f: [4] to [6] have 5 not in the range of f?

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Q: The function g is defined by the following rule. -()- IN g (x): %3D 6. Find g(x) for each x-value in…

A: Topic - functions

Q: The domain of the function f(x) = cosh + 19) + cosh¯1( 19 - ) is [-378 , A], Then The value of k =…

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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: If the function f(x) is even, which of the following is ze an O bn ao nothing is zero

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Q: Suppose, we want to define functions from set Ato set B Given that, |B| = n= 20 > 15 = m =HAN many…

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Q: The domain of the function f(x)= cosh"'(x/ 3) is Select one: O[3,) O[0,3] O None O[-3,3 ] OR-{3}…

A: The domain of the function f(x): The set of values of x for which the function f(x) is defined.

Q: 3. Determine if the function is even, odd or neither. 1 s(x) - (x'+x*}° а.

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Q: VII. Given that the domain of a one-to-one function f is (-3, 4] and the range is(-1,5). 12.) State…

A: Please refer the attached image for complete solution.

Q: Consider the piecewise function f(x) defined by 6 — 2х if x 4 х? — 16 For which x E R is f(x)…

A: Given function is fx=6-2x                            , if x≤4x-4x+4x-6x2-16    , if x&gt;4

Q: Use the IVT to show that f(x) = x 3 + x takes on the value 9 for some X in [1, 2].

A: Given- fx=x3+x To use- The intermediate theorem to show that the above function takes on the value 9…

Q: Find the rule for (f ogoh)(x).

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Q: The product of an odd function with an even function is even * O True O False

A: Given statement,   The product of an odd function with an even function is even.

Q: Suppose that the functions u and w are defined as follows. u (x) =x²+4 w (6) - /x+5 Find the…

A: givenu(x)=x2+4w(x)=x+5therefore(u+w)(x)=x2+4+x+5(u-w)(x)=x2+4-x+5

Q: Which among the following is an even function     x2 + 1     (x + 1)2     x2 + x     (x +…

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