4).a) Consider the function f (x) = x – 2e¬* + 1 for x 2 0.i) Show that the function is increasing and that its graph is concave down.ii) Examine f (x) as x → ∞ and sketch the graph of y = f(x). Clearly show the equationsof any asymptotes.iii) On the same diagram, sketch the graph of the inverse function y = f-²(x).%3Div) Find the x value of the point of intersection of the two curves.

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Answered: 14). a) Consider the function f(x) = x…

14). a) Consider the function f(x) = x – 2e-* +1 for x 2 0. i) Show that the function is increasing and that its graph is concave down.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 54E

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Question

4).
a) Consider the function f (x) = x – 2e¬* + 1 for x 2 0.
i) Show that the function is increasing and that its graph is concave down.
ii) Examine f (x) as x → ∞ and sketch the graph of y = f(x). Clearly show the equations
of any asymptotes.
iii) On the same diagram, sketch the graph of the inverse function y = f-²(x).
%3D
iv) Find the x value of the point of intersection of the two curves.

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Step 4: Part (iii): The sketch of the inverse of f(x).

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