Is function composition commutative?

Q: Consider the functions f(x) = x + 6 and g(x) = V-x + 6 . Determine each of the following. f o g(x)…

A: Given that f(x)=x+6 g(x)=√(-x+6)

Q: Let f(x) = x² - 6x and g(x) = 4 - x². ▪ (f+g)(4) = (f-g) (4) = (fg)(4) = (4) (4)

A:

Q: f(x)-f(a) Evaluate the difference quotient x-a function and simplify your answer as much as…

A: To find the diffrence quotient for f(x)

Q: Find the Green's function: G+ 16G= 8(x-5), G(0,5) = 0 G (2,5) = 0

A: The general solution to the homogeneous equation is Gh​(x)=Acos(4x)+Bsin(4x)Substituting (x=2π​)into…

Q: An exponentional function takes the form y= ab x . What does the "a", and "b" represent?

A: solution:-

Q: The translation represent f(x) + 2.

A:

Q: For f(x) = x2 +3 and g(x) = x² - 7, find the following functions. a. (fo g)(x); b. (g o f)(x); c.…

A: f(x)=x2+3 and g(x)=x2-7

Q: 4 m 8 9 10 11 12 + -12-11-10-9/-8-7-6-5 -31-2-1 Give the equation for the function whose graph…

A: The graph of function f(x) is given,The aim is to write the equation of the function f(x).

Q: Evaluate the function f(x) = x-7 at the given value of the variable. a. f(10) b. f(2) a. f(10) =…

A:

Q: How do I find f(x+h)?

A: We plug x+h in place of x

Q: Given the following two functions, is f(x) - g(x) = g(x)-f(x) true for all functions? f(x)=x²-9,…

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Q: Evaluate the function h(x)=x²+5x for the given value of x. h(a-5)=?

A:

Q: Rewrite h(x)=- Vx+3 in terms of f and g. 3.

A:

Q: State the end behavior of the function f(x) = -9x + 5x – 7x³ + 3x? – 6x As x - o, f(x) → Preview As…

A:

Q: Consider the function f defined by f(x) = (3 – x)(4 + 3x). What is f(-3)?

A: Given  f(x)=(3-x)(4+3x)

Q: Explain what it means for a function to be (1) and give an example of such a function.

A:

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: Let f(x) = 5x + 8, function g be defined by {(2, 3), (3, 5), (5, 2)}, and function h be defined by…

A:

Q: Evaluate the function for f(x) = x + 3 and g(x) = x2 – 2. (f + g)(-8) (f + g)(-8) = Need Help? Read…

A: f(x) = x+3  g(x) = x2 - 2

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.