The graph of f(x) is shown below: (1, –2) (0, –4) (2-4) (-2 4). (-1, –6) 1. To make the graph of f(x) invertible, the domain of f(x) is restricted to [a, 1]. What value of a gives you the largest possible domain over which f(x) is invertible? Do not include spaces, units, or commas in your response. Type answer here. Be careful with spelling. 2. To make the graph of f(x) invertible, the domain of f(x) is restricted to [-2, b]. What value of b gives you the largest possible domain over which f(x) is invertible?

Q: The equation of a quartic function with x-intercepts at 1 (order 2), -3 (order 1), 2 (order 1) and…

A: Let's find.

Q: Find the absolute maximum and minimum of f (x)=x* – 2x -x - 4x +3 on the closed interval [0, 4]. а.…

A: fx=x4-2x3-x2-4x+3 Differentiating wrt x, we get  f'x=4x3-6x2-2x-4 Putting f'x=0, we get…

Q: (a) Let f(x) = tanx- 2, g(x) = x5 + x³ and h(x) = Vcsc5x. Then find %3D the f(g(h(x))), using chain…

A:

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A: Attached below.

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Q: Q3/ 1- Let f: Zn → Z10 define by f(x) = 2x+2. Is fhomomorphism or not, explain your answer.

A: Given :-  let f : ℤn → ℤ10 define by f x = 2x + 2.  To Determine :-  Is f homomorphism or not.

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Q: (b) A continuous function f : [0, 1] → R such that its graph (r, f (x)) C R² is not closed.

A: The given statement, "A continuous function f:0,1→R such that its graph x,fx⊂R2 is not closed" is…

Q: The function f(x) is invertible. Find (f-1)' (-8) given that f(x) = -x³ – 4x – 3.

A: f(x) = -x3-4x-3 We will use the formula for the derivative of the inverse function: f-1'x0=1f'(x0)…

Q: Show that I (x) = 2x - 18 is invertible. What are the domain and range of f-1

A: fx=2x-18 Now consider, fx1=fx2,                   where x1, x2∈ℝ⇒2x1-18=2x2-18⇒2x1=2x2⇒x1=x2…

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Q: 3. Let f: A-→ B and g : B A be functions. Suppose that y = f (x) if and only if r =g (y). Prove that…

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Q: a continuous function f such that f(4) = 4, f'(4) = 0, ƒ'"(x) 4 is:

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Q: Show that f(x) = (x-2) / (x+3) is invertible and find its invcerse. (a) What is the domain of f? The…

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Q: (a) Let f: R" → R be a function given by f(x₁, 2,...,xn) = x²₁₁x²2x², where n = 1. Show that the…

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Q: 22. Find a and d for / «) = acosx+d such that the graph of f matches the figure. 3+ 2+ 1+ -3.14…

A:

Q: A natural cubic spline S for a function f is defined by +3 x² x 3 + 3 2 1≤x≤2 2≤x≤: 3≤x≤ 5(x) = - 12…

A: Given, A natural cubic spline ,s for a function.…

Q: Let g(z) = (- 2)(# - 3)2. Then g has a local maximum at a =

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Q: Discuss the continuity of the function g(x). 1 +- x 2 Vx- 2, Identify if the function g(x) is…

A: To check the continuity at x=1 we will find limx→1-g(x) and limx→1+g(x).…

Q: 2 The function defined by f(x)= x-3x for all real numbers x has a relative maximum at x = %3D

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Q: Sketch the graph of a function f that satisfies all of the given condi- tions. • There is a jump…

A: To sketch a function fx satisfying the following conditions limx→∞fx=-∞limx→-∞fx=-1f'3=0f'1=1f'4=-2…

Q: 9. Use the given graph of f (x) x2 to find a number 8 such that %3D if |x – 1| < 8 then |x2 – 1| <;…

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Q: 7) Find the absolute maximum of the function f on (0,0) f(x) =10xe2* %3D

A:

Q: Find the linearization at x = a. f(x) = 9x*, a = 1 %3D (Use symbolic notation and fractions where…

A: We have to find the linearization of the given function.

Q: 20. Use the following information to sketch the graph of the continuous func- tion y = f(x) whose…

A: First observe that the function is continuous and its domain is all real numbers.Start by plotting…

Q: 2. Let g : R → R be a bounded function and define f : R\ {0} → R by 1 f(x) = g(x)+ x2 Using only the…

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Q: The antiderivative of f (x), which is F (x), exhibits an odd symmetry, i.e., it satisf ies the…

A: Let's find.

Q: Let f₁(x) = x² and f₂(x) = x³. Complete the Wronskian for these functions. |x² w(x², x5)= 2x

A: Wronskian is a deteminant which is test for proving whether solutions are linearly independent or…

Q: 1. Determine whether k(x) is continuous at a = 3, where x + 3, x 2.

A: Left-hand limit of f(x) at x=a is represented by limx→a- f(x) and it can also written as limh→0+…

Q: True or False A function f has a local maximum at c if there is an open interval I containing c such…

A: We know that, from the definition of local maximum or relative maximum, we say that f has a relative…

Q: The absolute minimum of f(x) =x² – 4x On [0,3] is y= %3D 540 .BO -4 .CO -3

A: We use first derivative test to find absolute minimum.

Q: Describe the end behavior of the graph. 20 16 12 4 3-3 12 16- 20 f(x)→-co as x→-co and f(x)→-co as…

A: Consider the graph

Q: (1) Let f(x) = 1,x > 0 with domf= R4+. Find the conjugate of function f(x). %3D

A: given fx=1x , x&gt;0 with domf=R++ claim- find the conjugate of function fx

Q: Find the global maximum and minimum of the function on the given interval:f(x)=x2−2x+5,x∈[−1,4].

A:

Q: The antiderivative of f(x), denoted by Fx), exhibits an odd symmetry i.e., it satisfies the property…

A: we have to find the anti derivative .

Q: 1. Determine whether k(x) is continuous at r = 3, where %3D x + 3, x 2.

A: Given  k(x)=x+3,  x&lt;0x2+1, 0≤x≤22x,   x&gt;2 To check the continuity we can use the graph as…

Q: 2. Find the global maximum and global minimum of f(x) = xe- on [0, 6].

A:

Q: 1 1. Let f (x) = x - 5, g (x) = V5 - x and h (x) = 2x 1 a) Determine the domain of f, g and h. b)…

A: We have to find the function

Q: Find the absolute maximum and minimum of the function f(x) = x3 - x2 +x %3D on interval [0,3]

A: Given function is f(x)=x^3 -x^2+x on the interval [0,3] first lets find critical points find…

Q: Find the global maximum and global minimum of the function f(x)=x2−16x on the interval [−4,−1].

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Q: (b) Find the global maximum and minimum values and indicate where they occur. f(x1,x2) = 2x, + x, –…

A: Given,

Q: A quadratic function f is given. f(x) = 1 - 10x - xr? (a) Express fin standard form. f(x) = (b)…

A: The given function f(x)=1-10x-x2

Q: find the value of ( ƒ ∘ g)' at the given value of x. ƒ(u) = 1 - 1/u, u = g(x) = 1/1 - x, x = -1

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Q: 5. Determine the Wronskian of the functions (x)=x2 and g(x)=3x2. For what values of x is the…

A: Please refer to the image below

Q: Find the global maximum and minimum of the function f(x)=√3−2x on the interval [−3,1).

A:

Q: 5. Find the domain of the function: y = In () x-4

A: y=lnx-1x-4

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.