Under what conditions imposed on functions the sum, difference, product and quotient of function will be function again.

Q: A wire length 23 is to be cut into two pieces and formed into a square and a circle. Let x represent…

A: Given that the total length of the wire is 23. That is, the perimeter of the wire is 23. Let x be…

Q: From each corner of a square tin, 12 inches on the side, small squares of side x are removed and the…

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Q: 8. Determine algebraically if the function is even, odd or neither. y = -2' - |-2°|

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Q: If f and g are both even functions, is f + g necessarily even? If both are odd, is their sum…

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Q: Assume that f is a one-to-one function. If f(3) = 5 and f(-1) = 4, what is f-1(5)?

A: f is one to one function and f(3)=5,f(-1)=4.

Q: Determine if the given function is homogenous or not: f(x,y) = sqrt(x-y)

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Q: Find all points of intersection between the graphs of the functions f(x) = (x + 5)(x-4) and g(x) = x…

A: Explanation of the answer is as follows

Q: can an even function be selv-inverse?an odd function?

A: Can an even function be self-inverse?an odd function?

Q: There can never be two functions f and g, where f ≠ g, for which (f ∘ g)(x) = (g ∘ f)(x).Determine…

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Q: What is the purpo

A: To determine: Purpose on adding h to the function.

Q: An environmental scientist found that the number of gallons of a pollutant in a lake is growing…

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Q: Determine whether  the following statement is true or false, and explain why. If ƒ′(x) >0 on an…

A: Given, f'(x)=0 since f'(x) represents slop[e of a function ⇒slope is positive

Q: represents

A: False

Q: Suppose f is a one-to one function. If f(4) = 3 , then f(3) is %3|

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Q: Suppose that P(x) represents the percentage of income spent on health care in year x and I(x)…

A: Given :- P(x) percentage of the income spent on health care in year x and I(x) income in year x.

Q: Evaluate the piecewise defined function at the indicated values. if x 5 f(-5) = f(-2) = f(4) = f(5)…

A: Given function is For x<-2 , f(x)=5x Therefore,

Q: x< -1 -1 <x< 0 x = 0 0 <x< 1 1, -x, f(x) = • 1, -x, 1, x 2 1.

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Q: What is the domain of the following function?

A: Given f(x,y) =4-x2-y2 - ln(y-x) + sin(x)Let g(x,y) =4-x2-y2 h(x,y)= ln(y-x) and t(x)=sin(x)

Q: * The product of two odd functions are even True False

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Q: Find all the numbers for which the function is discontinuous.

A: A function is discontinuous at a point if the functional value is not defined at that point. There…

Q: 5. When functions are defined by more than one equation, they are called functions.

A: When functions are defined by more than one equation, they are called piece-wise defined functions.

Q: Ser Jepp has a favorite function defined by f(x)= px+q^x. If f(1) = 4 and 4f(2) = 44, then give…

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Q: Suppose that V(x) represents the number of violent crimes committed in year x and P(x) represents…

A: Given  V(x) represents the number of violent crimes committed in year x  P(x) represents the number…

Q: Discretise the same function tained previously.

A: Given,              ϕ=x(x-3.5)(x+3)+30

Q: The 2014 domestic postage rate for first-class letters weighing 3.5 oz or less is 49 cents for the…

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Q: Find the domain of the following function: h(x)=√(2x-3)(x+4) Be sure to write your answer in…

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Q: Suppose that the selling price of a company's primary product is 1600−0.3x dollars per unit when x…

A: Demand function represents the relationship between the quantity demanded for a commodity (dependent…

Q: A landowner wishes to use 6 miles of fencing to enclose an isosceles triangular region of as large…

A: The isosceles triangular region must have fencing of 6 miles and we must have largest possible area.…

Q: Give one way to restrict the domain of the function f (x) = X4-2to make the resulting function…

A: Given function is: fx=x4-2fx=x2

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

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Q: Find the function value. 1.If F(x)= x³-2x²-x+1, find F(2)and F(-2). 2.If F(x)= x²-3/x-1,find F(3)…

A: 1. Given function: Fx=x3-2x2-x+1 At x=2: Fx=x3-2x2-x+1F2=23-2×22-2+1F2=-1 At x=-2:…

Q: About the Discontinuity of a function, kindly provide 5 Questions about it with solutions.

A: For a function f(x) to be continuous at a point x=a, it must satisfy the two of the following…

Q: b) Write a piecewise-defined function for the income of an author (f(x)) who earns $10 for each book…

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Q: Indicate whether the two functions are equal. If the two functions are not equal, then give an…

A: The given 2 functions are as follows. f:Z×Z→Z where fx,y=x+y g:Z×Z→Z where gx,y=x+y Both the…

Q: x = 0 is not a function. Select one: True False

A: A function is defined as the relationship between an input and an output. In function each input…

Q: Suppose that P(x) represents the percentage of income spent on health care in year x and I(x)…

A: To determine function H that represents total health care expenditures in year x

Q: Which description below is true for the the domain of the following function?

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Q: A function has a zero at X = 8, indicating what?

A: Given, A function has a zero at X=8

Q: The owner of a luxury motor yacht that sails among the 4,000 Greek islands charges $550 per person…

A: Consider the provided question,(a)Given at least 20 people sign up for the cruise and charge for the…

Q: Is function composition commutative?

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Q: If f(x) = x2 and g(x) = x − 3, find the composite functions f ○ g and g ○ f. You must show ALL…

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Q: if x1

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Q: 7, find out whether the following functions are analytic 24. y - ix x² + y²

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Q: Since f'(x) is a function, f'(x) has its own graph, one that is based on the behavior of f(x). True…

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Q: A function is defined as: (-1 for - 3<x< 0 %3D +1 for 0 < x < 3

A: Given, f(x)=-1    for  -3≤x&lt;0+1    for    0&lt;x≤3 Given function is a piecewise defined…

Q: Show the following concepts are true by providing specific examples of the functions and apply the…

A: Give examples: For f∘gx=g∘fx. Calculation: Assume fx=x2 and gx=x, then f∘gx can be obtained as,…