Show that f and g are inverse functions (a) analytically and (b) graphically            f(x) = 16 − x2,    x ≥ 0,     g(x) = √(16 − x)

Q: Find the inverse of the function on the given domain. f (x) = (x – 16)2, [16, 0) ab sin (a) o (2) =…

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Q: Disprove the statement ln x / ln y = ln x - ln y,  by, a) Letting y equal a positive constant of…

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Q: Determine analytically the point (s) at which the graph of the function has a horizontal tangent. x2…

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Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

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Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

A: We have given fx=1-x3-6x5 By differentiating the function, f'x=-3x2-30x4=-3x21-10x2 Now, we find the…

Q: 1. Determine if the function is even or odd x*+1 g(x) = f(x) = sin x x3-2x

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Q: Find f"(x) for a) f(x)= lnx - ln(1/x)

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Q: Consider the function, f(x) = (x + 1)ln(5x² + e). Without finding explicitly the inverse of f(x),…

A: Given : fx = x+1ln5x2+e

Q: 4. Let a be a real number such that 0 < a < 1, and let f(t) = eat – t where t e R. a) Find the…

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Q: Differentiate  f and find the domain of f f(x)  =    ln ln ln x

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Q: Show that g : B → A, g(x) = √ln x is the inverse of f. Why is f^−1(x) 6 ≠ −√ln x?

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Q: Find a formula for the inverse of the function. \\ f(x) = f-¹(x) = 1+e 1-e

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Q: Find the first derivative f' and the original function f. f"(x) = x³ – 10x + 6, f' (0) = 7, f(0) = 2…

A: Note: according to our guidelines we can answer only first question

Q: Find the inverse of the function on the given domain. f(x) = (2 – 10)2. [(10, 0) b sin (a) f\(2) =

A: Solution: The objective is to find the inverse of the given function

Q: 1) Find the hundredth derivative of p (x) = (x + x° + x')'º(1 + x²)'' (x³ + x° + x'). Justify your…

A: Here we have to find the hundredth derivative of p(x)=(x+x5+x7)10(1+x2)11(x3+x5+x7) .

Q: The best suitable method to approximate a zero of the function f(x) = e* – 1 is:

A: Given f(x) = ex - 1

Q: The best suitable method to approximate a zero of the function f(x) = e* – 1 is: |

A: Given,                 f(x)=ex-1

Q: МАТ 115 1.Find the derivative a. f(x) =x' In x b. f(x) = (x'+x-1) %3D с. f(x) d. f(x) = 4e*- x 3D20…

A: As per barlteby guideline for more than one sub question asked only first three are to be answered…

Q: 1. Find the first derivative of the function g(x) = 6x+ 27r'+36x. g'(x) 18x + 54r +36 2. Find the…

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Q: Suppose that f(x) I + 6 is differentiable and has an inverse for æ > 1 and f (2) = 8. Find (f ')'…

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Q: Let f(x) = x + ln(x) and g(x) its inverse. Find g′(1).

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Q: 1. Find the differentiation of inverse function for the following functions. (a) f(x) = 2x³ - 5 (b)…

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Q: A. What is the domain and the range of the inverse function of f(x) = 4[sin(n – 2x) – 1] %3D -

A: It is asked to find the inverse of the given function.

Q: 十2, What is the inverse function of y = ? T-2 Oy= 2(+1) 7-1 %3D 2z-2 O y = -1 2(+1) O y= -1 2-1

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Q: Find the domain of the function. g(x) = ln(x - 1)

A: A function is a relation between an input variable and an output variable wherein each input…

Q: 1. Consider the function f ( x ) = 1 + 1/10 x3 + 1/25 x5 .  Select any point ( a , f -1 ( a ) ) on…

A: Given function : f(x)=1+110x3+125x5 To solve the given problem first we need to find the inverse of…

Q: if f(x) = x²√√In x² A. f'(x) = B. f'(x) = c. f'(x) = D. f'(x) = find the derivative of this function…

A: Given,            fx=x2lnx2xTo find : Find the derivative of the given function.

Q: 1. Consider the function f(x) given by its graph at which the points C, E and H are the inflection…

A: Let's find.

Q: The (blue) graph of an invertible function, f(x), is given. Drag the (green) points from the top…

A: Graph of inverse function is

Q: Find the domain of the function 3x -1 A. f(x)= 1- 2x + 3 sin 2.

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Q: Find the derivative of f(x) = xe-2x O (E) None of these O f'(x) = x²e-22 re (-2) O f'(x) = 2x²e-2r O…

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Q: (a) Express the new function m(x) = ln in terms of the original function g(x) In(x). m(x) :

A: Given- mx=lnx2and gx=lnx To find- The value of mx in terms of gx. Formula used- lnab=lna-lnb

Q: - Show that f(x)= E ƒ(x), where E is a constant and f(x)= e²x + e2x

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Q: 8. Suppose that g is the inverse of f and that both f and g have nonzero derivatives up to order…

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Q: show that the function f(x) = (x − 1)e^x^2 has an inverse, and find prime of (f^-1) (0).

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Q: 1. Compute the first, second, and third derivative of a. f(x) = x² In(x+1) b. h(x) = x² sin x

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Q: Consider the function f(x) = i + x². How does this function essentially behave for large positive…

A: The Given Function f(x) contains rational function x/(x2+1) and polynomial function function…

Q: Find the domain of the function. g(x) = ln ( 1/x - 5)

A: given,

Q: How does a domain restriction placed on a non-invertible function affect its inverse? Drag a…

A: Given query is to find the inverse and it's domain.

Q: A) Find the Domain of the following functions 1) f(x) = vx – 3+ V5 – x 2) f(x) = 3 – log2 x² – (log2…

A: Note: we answer up-to 3 multiple subparts. Please resubmit question which you would like to get…

Q: 8) Find (f-1)'(a) for each (the derivative of the inverse of function f). f(x) = x³ + 2x + 3, a = 0…

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Q: 1 The function h(x) : can be expressed in the form f(g(x)), where g(x) = (x – 9), and f(x) is %3D x…

A: NOTE: Refresh your page if you can't see any equations. . but here

Q: if y(x)=Power[x,2]+3 and x(t)=3t-1, what is y(x(t))??? and how does functional notation make sense??…

A: Given yx=Powerx, 2+3 and xt=3t-1

Q: Find the domain of the function: h(x) = ln(x - 3)2.

A: Given: hx=lnx-32 By using the property of logarithmic function, the given function can be expressed…

Q: 1. Sketch the reciprocal of the function f (x) = x - 6.

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Q: The functions f (x) = e² and g (x) = ln x are inverses. %3D Therefore, what is the value of eln(8)?

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Q: Find a formula for the inverse of the function.\\ f(x) 1+e" 1-ez ' f' (æ) =

A: Let f(x)=y f(y)=x

Q: Find the slope of the tangent line to its inverse function f^-1 at the indicated point P, and find…

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Q: 5 Let f(x) =x -e*. Find the value of x for which the second derivative f“equals zero. 2

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.