Hello I need help solving these questions. Decomposition of Functions: We can write it as a composition of two simpler functions **Many answers**Find functions f(x) and g(x) so that the given function can be expressions as h(x) = f(g(x)).%3DEX: h(x) =|x – 5|+8EX: h(x) = 7+(4x–1)**Hint: Let g(x) = x -5**Hint: Let g(x) = 4x - 1EX: h(x)=EX: h(x) = 3- 2x + 64.(x- 2)?

Given:- h(x)=f(g(x)) h(x)=|x-5|+8 h(x)=7+(4x-1)3 h(x)=4/(x-2)3 h(x)=3-√(2x+6)

Answered: Decomposition of Functions: We can…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.7: Operations On Functions

Problem 48E

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Similar questions

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Geometry The perimeter of a rectangle is 200meters. (a) Draw a diagram that gives a visual representation of the problem. Let x and y represent the length and width of the rectangle, respectively. (b) Write yas a function of x.Use the result to write the area A as a function of x. (c) Of all possible rectangles with perimeters of 200meters, find the dimensions of the one with the maximum area.
Minimizing a Distance When we seek a minimum or maximum value of a function, it is sometimes easier to work with a simpler function instead. Suppose g(x)=f(x) where f(x)0 for all x. Explain why the local minima and maxima of f and g occur at the same values of x. Let gx be the distance between the point 3,0 and the point (x,x2) on the graph of the parabola y=x2. Express g as a function of x. Find the minimum value of the function g that you found in part b. Use the principle described in part a to simplify your work.
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Population Growth: The growth G of a population over a week is a function of the population size n at the beginning of the week. If both n and G are measured in thousands of animals, the formula is G=0.25n2+5n, a. Make a graph of G versus n. Include values of n up to 25 thousand animals. b. Use functional notation to express the growth over a week if the population at the beginning is 4 thousand animals, and then calculate that value. c. Calculate G(22) and explain in practical terms what your answer means. d. For what values of n is the function G increasing? Determine whether the graph is concave up or concave down for these values, and explain in practical terms what this means.
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