Use the pair of functions to find  f(g(x))  and  g(f(x)).  Simplify your answers. f(x) = |x|,     g(x) = 7x + 5 f(g(x)) =       g(f(x)) =

Q: The function C(x)=10x+5,000 represents the cost to produce x number of items. How many items should…

A: SOLUTION-

Q: Write g ( x ) in terms of f ( x ). f ( x ) = 3x + 5    g ( x ) = 3x - 1

A:

Q: Find the intervals where the function f(x)= x3- 3x 2+3 is increasing and intervals where the…

A: The given function is f(x)=x3-3x2+3. It is required to find the interval in which the function is…

Q: 2) f(x) = -5x² + 3x -7, find: f(x + h)- f(x)

A: According to the problem, we have

Q: f(x) = x²e-3*,

A:

Q: Find f' (2) for f(x) = x²e2¤-3

A: To find the derivative of the given function we have to apply chain rule of differentiation and the…

Q: For the function f (x) = (*-2)* x+2 , find f-'(x).

A:

Q: or f (x) = e-*+3, find f'(2.5). %3D

A: Given query is to find indicated derivative.

Q: What is g (f (2)) ? f (x) = 3x2 + 1 g (x) = -x + 2

A:

Q: Find (f-g)(x). Simplify the result. f(x) = x²-6x + 3 g(x) = 3x2 - 5

A: Given that, fx=x2-6x+3 and gx=3x2-5.

Q: Solve for g'(x).

A: Theorem used:

Q: Find the domain of the function: f(x) = x2 + 3x - 17

A: Given function:

Q: What is f (g (3)) ? f (x) = 3x² + 1 g (x) = -x +2

A: f(g(3)) also written as fog(3) is know as composition of function. Here, x-values are input in g(x)…

Q: How do I find the x-coordinate of the point of inflection of f(x)=x(x-8^(1/2))?

A: The given function is,

Q: At what value of x does the function f (x) =x- 3x-9 x change from decreasing to increasing?

A:

Q: What is the value of x if f(x) = -3? %3D

A:

Q: using its equation. f(x) =(4x5)– 3x + 2x³ Justify how you know here:

A: End behavior is determined by the degree of the polynomial and the leading coefficient.

Q: Determine the image of the function - 12x + 27 - f(x) = x2 – 4x + 5 - for all æ E R. Solve the…

A: Given: f(x)=x2-12x+27x2-4x+5  for all x∈ℝTo determine the images of f(x)i.e, range set of f(x)

Q: for what value of x does the function g(x)=1/3x3-2x2 attain the point of inflexion?

A:

Q: Differentiate the function. f(x) (9x2 15x)e* = f'(x)

A: First simplify the given function as follows.

Q: The range of a function f(x) = 9x – 15 is {-42,39}. Wh %3D

A: Actually from my point of view you want to know the domain of f(x)  because in this question range…

Q: f(x) = 9(x2)

A:

Q: The range of f(x)= 3+|x| is

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Q: For what value of x does the function g(x) = -x – 2x? attain the point of inflexion?

A: i have used the necessary and sufficient condition for point of inflection and obtained x=2 is…

Q: (x* -3x,ifx 22 Find g(x). g(0). g(-2) x+2, ifx < 2

A:

Q: Find the domain of the function f(x)=17x+3f(x)=17x+3. What is the only value of x not in the…

A: the function given to us is  f(x) = 17x + 3

Q: B) find the Domain and Range f(x) = Vx – 3x²

A:

Q: Identify the domain and range: x – 2 1. f(x) = x2 – 5x + 6 -

A: Given,         fx=x-2x2-5x+6

Q: find the Domain and Range: f(x) = V1-2x

A:

Q: What is the point of intersection for f(x) = 2* and g(x) = A (1,0) (1, )

A: Here we have to find the point of intersection of f(x)=2x ............................... (1)  and…

Q: Use the functions f(x)=4x+1, g(x)=2x2−6x, h(x)=−x2+3x−19.  Find (f - h) (x)

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Q: Find the points of inflection. 7) f(x)=x√√9-x2

A:

Q: To find g(x + 1), what do you substitute for x in the function g(x) = 8x − 2?

A: To find g (x + 1).

Q: What is the end behavior of the function f(x)=2e^x? Select the two correct answers.

A:

Q: Given the function f (x) = -3x + 2, what is f (2)?

A: Given:  The function f (x) = -3x + 2

Q: Find the function f(x) = -4x^2 + 3x-1 1. F(-2)

A:

Q: find the range of f(x)=x−4/x2−16

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Q: How many points of inflection does the function f(x)=x8-x2 have?

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Q: Differentiate the function: a) f(x) = e10z–2» = el003-2x b) f(x) = Vª + 2 c) f(x) = (4x7 – 2x*)5

A:

Q: What is the degree of the function g(x)=-2x(2x–1)(r² +1)* ?

A: We have to solve the problem

Q: raph the function. 2x +3, if x < 0 14) f(x) = . x2 - 4 ifx2 0

A: The graph is a combination of a straight line in case of 2x+3 and a parabola in case of x2-4:…

Q: 4) Is y = -3x² + 12, x 20 a one-to-one function? Why or why not?

A: For one -one function F(x1)=F(x2) then x1=x2

Q: For this exercise, you will demonstrate the tests to show that y 6x° + 11x* + 5x° is neither an even…

A: The solution is given below:

Q: Find the stationary points and stationary values of the function f (x)=2x'+x² - 20x +5.

A:

Q: The profit function for a company that produces shoes is given by y = - 2x ^ 2 + 12x +23, where "y"…

A:

Q: Determine the image of the function x2 – 12x + 27 - f(x) = x² – 4x + 5 for all æ E R. Solve the…

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Q: Find the point on the graph of the equation f (x) = x² – 8 that is closest to the point (0, -2)

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Q: Find (f -g)(x). f(x) =x² +3, g(x)= V5-x

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Q: or what value of X does the function g(x) = 1/3 X3 - 2x2 attain the point of inflexion?

A:

Q: Find the point of dimminshing returns (x,y) for the function R(x)=4000-x3+48x2+500x, 0<x<20, where…

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.