For the real-valued functions =f(x)=√5x+40 and g(x)=x−3, find the composition  (f∘g) and specify its domain using interval notation.

Q: For the functions f(x)=2x−2 and g(x)=6x^2−3, find (g∘f)(x).

A: Explanation of the solution is given below...

Q: For the function f (x) = x4 - 4x3 + 5, find the local and absolute extrema and any points of…

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Q: The total revenue for Dante's Villas is given as the function R(x)=500x−0.5x2R(x)=500x−0.5x2, where…

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Q: What is a reasonable domain for the function f(x) = 14x + 12?

A: A reasonable domain for the function f(x)=14x+12 is 0<x<8

Q: For the functions f(x) = 2x - 4 and g(x) = 3x² + 2x, find (gof)(x).

A: The answer as follows:

Q: For the function f(x)=x2−8x+8, use f(x)=−4 to find two points on the graph of the function.

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Q: For the function f(x) = V - 6, find f-(x).

A: Given : f ( x ) = x ( 1/4)  - 6  find : f - 1  ( x ) = ?

Q: For the function f(x) = x6 – 10x4 , find the points of inflection.

A:

Q: For the functions f(x)=2x−3 and g(x)=3x2−2, find (f∘g)(x).

A: f(x)=2x−3 and g(x)=3x2−2To find (f∘g)(x)

Q: For the function f(x) = x3/3-x2- 24x + 19 (i) Determine the turning points and the values of the…

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Q: Find the domain for the functions 1. f(x) = 8– V3x – 7 -

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Q: For the function f(x)=8x2−18x+5, find x when f(x)=−4.

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Q: For the functions f(x)=3x−4 and g(x)=6x^2+5, find (g∘f)(x).

A: Composite of two functions f(x) and g(x) is defined as:  (gof)(x) = g(f(x))

Q: For the functions f(x)=3x2−3 and g(x)=2x3+2, find (f∘g)(0) and (g∘f)(0).

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Q: For the function f(x) = , find f-1(x). %3D 72 Of (x) = 7a Of (x) = (7x)²

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Q: 13. For the function f(x) = r² – 3r + 2, find the difference quotient.

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Q: Find the domain for (f- g)(x) when f(x) = v9x +7 and g(x) 10 8x

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

Q: For the functions f(x)=6x−4 and g(x)=2x^2+5, find (g∘f)(x).

A: Given functions are: fx=6x-4gx=2x2+5

Q: For the function f(x) = 4x3, find f'(2). %3D

A: f(x)=4x13=yFor inverse, interchange x and y and solve for y

Q: For the function f(x)= 3x^4+12x^3+13, where is f(x) increasing?

A: Solved below

Q: What is f(3) for the function f(x) = 4x + 7? f(3) =

A: Put value in function

Q: For the function f(x) = x² + 5x – 2, find (a) f(3) (c) -f(x) f(x + h) – f(x) (b) f(-x) (d) f(3x) (e)…

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: For the functions f(x)=x2−6x−16 and g(x)=x+2, find (f/g)(x) and (f/g)(−3).

A: Given data:   The first function given is f(x)=x2-6x-16. The second function given is g(x)=x+2.…

Q: For f(x) = 4x + 3x2 f (21)– f (x2) x - 1, the range of values is x1 - x2

A: given  f(x)=4x3+3x2-x-1range of f(x1)-f(x2)x1-x2 is range of slope of f(x) the slope of f(x) will be…

Q: For the function f(x) = 3x-2x-3x +2, find "(X). Then find f"(0) and "(4).

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Q: Find the real zero of the function f(x)= 5x - 30.

A: Given function                    f(x)=5x-30

Q: For the function f(x)=8x2−18x+5, use f(x)=−4

A:

Q: . For f(x) = 5x - 8 and g(x) = x2 - 3x + 4, find (g - f)(x)

A: given,         f(x)= 5x - 8gx=x2-3x+4

Q: Let f(x) be the function 2a² – 4x + 11, Then the quotient f(2 + h) – f(2) - can be simplified to ah…

A: The equation of line between two points;(4, -3) and (-3, 0)f'(4)=0+3-3-4=-37passes through (-3,…

Q: For the function ​f(x)=5x3−9x2+7x+9​, find f′′​(x). Then find f′′​(0​) and f′′​(9​)

A: We have to apply simple differentiation rules to solve the problem If we have f(x) = xⁿ f'(x) = xⁿ-1

Q: For the function: f (x) = 3x² – 4x - 8, find and simplify f(x + h) – f(x).

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Q: For the functions f(x)=−7x+3 and g(x)=3x2−4x−1, find (f⋅g)(x) and (f⋅g)(1).

A:

Q: For the function f(x,y) = 5x - 6y - 6, find - of and

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Q: For the function f(x) = 3* find fx-2)

A: Given that: f(x)=3x.   NOTE: As per our answering guidelines, we can only answer 1 question or 3…

Q: For the function f(x) = x3/3-x2- 24x + 19. what is the value over which the function is concave…

A: fx=x33-x2-24x+19    Now, first derivative is  dfdx=ddx(x33-x2-24x+19)  dfdx=x2-2x-24    And, second…

Q: For the function f(x)=8x2−18x+5, use f(x)=−4 to find two points that lie on the graph of the…

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Q: Given the function f(x) = - + v , find f'(4). Express your answer as a 2 single fraction in simplest…

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Q: Find the domain of f

A: f(x)=2x+7

Q: For the function z) =-3x+8 determine x when Ax) =-25,

A:

Q: For the function f(x) = 7x", find ƒ-'(x).

A: Given,         The function is fx=7x7 .

Q: For the function f(x) = 7x° - 2x2 + 5x+6, find f"(x). Then find f'"(0) and f"(3). f"(x) =

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Q: For the function f(x) = 5x³ – 3x°, |

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Q: For the function: f(x) = 2x + 8, f(æ) – f(a) с — а -

A: Given that f(x) =2x+8 .First we evaluate f(a) then substitute in the given expression.

Q: For the functions f(x) = 3x – 1 and g(x) = 6x² + x, find (f • g)(x).

A: Given : fx = 3x-1gx = 6x2+x

Q: Given the function f (x) = – x² +x, then what is f(x – 3) as a | | polynomial?

A:

Q: For the function f (x) = 2x³ – 3x² – 12x, find the points of inflection of f (x)

A: the point of inflection is 1/2

Q: For the functions f(x)=2x+1 and g(x)=3x2+4, find (f∘g)(−2) and (g∘f)(−2).

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Q: Given the function f(x) = 4x² - 3x + 5, find and simplify the difference quotient ( f(x+h)-f(x))/h.…

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Q: For f(x) : Vx+5 and g(x) = x + 8, the domain of х-9 |x is?

A: We can find the answer as below.

Q: For the functions f(x)=4x+5 and g(x)=4x^2−4x, find (g∘f)(x). (gof) (x)=

A: We need to find the composite function when the individual functions are given. while calculating…

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.