1) Use f(x) = -2 In(x + 1) to do the following: d. Find f-1 e. Find the domain and range of f-1 f. Graph f-1

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**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.
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
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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