Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Question
**Problem 1: Inverting and Analyzing the Function** Given the function \( f(x) = -2 \ln(x + 1) \), perform the following tasks: **d. Find the Inverse Function \( f^{-1} \)** Find the expression for the inverse of the function. **e. Determine the Domain and Range of \( f^{-1} \)** Identify the domain and range for the inverse function. **f. Graph \( f^{-1} \)** Use the provided coordinate grid to sketch the graph of the inverse function. The grid is a standard Cartesian plane with both horizontal and vertical axes, marked with equal increments, ready for plotting functions. The center of the grid is represented by the intersection of the x and y axes.
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Transcribed Image Text:**Problem 1: Inverting and Analyzing the Function** Given the function \( f(x) = -2 \ln(x + 1) \), perform the following tasks: **d. Find the Inverse Function \( f^{-1} \)** Find the expression for the inverse of the function. **e. Determine the Domain and Range of \( f^{-1} \)** Identify the domain and range for the inverse function. **f. Graph \( f^{-1} \)** Use the provided coordinate grid to sketch the graph of the inverse function. The grid is a standard Cartesian plane with both horizontal and vertical axes, marked with equal increments, ready for plotting functions. The center of the grid is represented by the intersection of the x and y axes.
Expert Solution
Check Mark
Step 1

Given that:

f(x) = -2ln (x+1) 

To find:

a) inverse of f(x) 

b) Domain and range of inverse of f(x) 

c) graph of f-1(x)

Calculations:

a) We find the inverse of f(x) 

Let y = f(x) 

So, x = f1(y)              ..(1)

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