Please solve parts e and f. Exercise II: ProfitConsider the function f(x) = 3 ln (x –- 1)–2r+7 on the interval (1, o0). Do not use graphicaljustifications in this exercise, but you can use a calculator to approximate values. When youdo, round to two decimal places.(a) Find lim f(x) and lim f(x).(b) Find the intervals where f is increasing or decreasing. Show all steps.(c) Is there a global minimum? A global maximum? If so, what are their coordinates?(d) Show that f has exactly two roots. If these roots occur at r = a and r = B, show that1.21 < a < 1.22 and 5.87 < a < 5.88. Clearly state the result(s) you are using here.(e) Now restrict the function to the interval [2.5, +0). Show that f has an inverse function,and find the domain and range of this inverse function.(f) ƒ actually represents the total profit (in millions of Euros) from the production andsale of x thousand motorcycles. Explain, in words, what the answers for parts (c) and(d) mean in this context. You can also approximate values for a and 3 based on theanswer in (d) (do not use a calculator to find a and B exactly).

(e) given fx=3lnx-1-2x+7 on [2.5,∞) solution let gx=f-1x replace x by fx we get, gfx=f-1fx…

Answered: (e) Now restrict the function to the…

(e) Now restrict the function to the interval [2.5, +). Show that ƒ has an inverse function, and find the domain and range of this inverse function.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.FR1: A Further Look: Limits

Problem 1E

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Question

Please solve parts e and f.

Exercise II: Profit
Consider the function f(x) = 3 ln (x –- 1)–2r+7 on the interval (1, o0). Do not use graphical
justifications in this exercise, but you can use a calculator to approximate values. When you
do, round to two decimal places.
(a) Find lim f(x) and lim f(x).
(b) Find the intervals where f is increasing or decreasing. Show all steps.
(c) Is there a global minimum? A global maximum? If so, what are their coordinates?
(d) Show that f has exactly two roots. If these roots occur at r = a and r = B, show that
1.21 < a < 1.22 and 5.87 < a < 5.88. Clearly state the result(s) you are using here.
(e) Now restrict the function to the interval [2.5, +0). Show that f has an inverse function,
and find the domain and range of this inverse function.
(f) ƒ actually represents the total profit (in millions of Euros) from the production and
sale of x thousand motorcycles. Explain, in words, what the answers for parts (c) and
(d) mean in this context. You can also approximate values for a and 3 based on the
answer in (d) (do not use a calculator to find a and B exactly).

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