Calculus: Graphical, Numerical, Algebraic: Solutions Manual

3rd Edition

ISBN: 9780132014144

Author: Ross L. Finney, Franklin Demana, Bert K. Waits, Daniel Kennedy

Publisher: Pearson Prentice Hall

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Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, c…

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Question

Chapter 1, Problem 69RE

To determine

To find: the domain of f.

Expert Solution

Answer to Problem 69RE

The domain is (2,∞) .

Explanation of Solution

Given information: Let f(x)=1−ln(x−2) .

Calculation:

The log of a negative number is undefined so x−2>0⇒x>2 ,so the domain is (2,∞) .

To determine

To find: the range of f.

Expert Solution

Answer to Problem 69RE

The range is (−∞,∞) .

Explanation of Solution

Given information: f(x)=1−ln(x−2) .

Calculation:

All logarithmic functions have a range of all real numbers so the range is (−∞,∞) .

To determine

To find: arc the x-intercepts of the graph of f.

Expert Solution

Answer to Problem 69RE

The x − intercepts is (2+e,0)≈(4.718,0) .

Explanation of Solution

Given information: f(x)=1−ln(x−2)

Calculation:

The x − intercepts are when y = 0, so:

0=1−ln(x−2)ln(x−2)=1eln(x−2)=e1x−2=e1x−2=ex=e+2.

The x − intercepts is (2+e,0)≈(4.718,0) .

To determine

To find: f−1 .

Expert Solution

Answer to Problem 69RE

f−1(x)=e1−x+2.

Explanation of Solution

Given information: f(x)=1−ln(x−2) .

Calculation:

To find the inverse, switch x and y and then solve for y:

x=1−ln(y−2)x−1=−ln(y−2)1−x=ln(y−2)ln(y−2)=1−xeln(y−2)=e1−xy−2=e1−xy=e1−x+2f−1(x)=e1−x+2.

To determine

To confirm: answer algebraically in part (d).

Expert Solution

Answer to Problem 69RE

Explanation of Solution

Given information: f(x)=1−ln(x−2) .

Calculation:

To functions are inverses if f∘f−1=f−1∘f=x .

f∘f−1=f(e1−x+2)=1−ln(e1−x+2−2)=1−(1−x)=x

f−1∘f=f−1(1−ln(x−2))=e1−(1−ln(x−2))+2=eln(x−2)+2=x−2+2=x

Therefore, f(x)=1−ln(x−2) and f−1(x)=e1−x+2 are inverses.

Chapter 1, Problem 68RE

Chapter 1, Problem 70RE

Chapter 1 Solutions

Calculus: Graphical, Numerical, Algebraic: Solutions Manual

Ch. 1.1 - Prob. 1QR Ch. 1.1 - Prob. 2QR Ch. 1.1 - Prob. 3QR Ch. 1.1 - Prob. 4QR Ch. 1.1 - Prob. 5QR Ch. 1.1 - Prob. 6QR Ch. 1.1 - Prob. 7QR Ch. 1.1 - Prob. 8QR Ch. 1.1 - Prob. 9QR Ch. 1.1 - Prob. 10QR

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - 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Prob. 61E Ch. 1.6 - Prob. 62E Ch. 1.6 - Prob. 1QQ Ch. 1.6 - Prob. 2QQ Ch. 1.6 - Prob. 3QQ Ch. 1.6 - Prob. 4QQ Ch. 1 - Prob. 1RE Ch. 1 - Prob. 2RE Ch. 1 - Prob. 3RE Ch. 1 - Prob. 4RE Ch. 1 - Prob. 5RE Ch. 1 - Prob. 6RE Ch. 1 - Prob. 7RE Ch. 1 - Prob. 8RE Ch. 1 - Prob. 9RE Ch. 1 - Prob. 10RE Ch. 1 - Prob. 11RE Ch. 1 - Prob. 12RE Ch. 1 - Prob. 13RE Ch. 1 - Prob. 14RE Ch. 1 - Prob. 15RE Ch. 1 - Prob. 16RE Ch. 1 - Prob. 17RE Ch. 1 - Prob. 18RE Ch. 1 - Prob. 19RE Ch. 1 - Prob. 20RE Ch. 1 - Prob. 21RE Ch. 1 - Prob. 22RE Ch. 1 - Prob. 23RE Ch. 1 - Prob. 24RE Ch. 1 - Prob. 25RE Ch. 1 - Prob. 26RE Ch. 1 - Prob. 27RE Ch. 1 - Prob. 28RE Ch. 1 - Prob. 29RE Ch. 1 - Prob. 30RE Ch. 1 - Prob. 31RE Ch. 1 - Prob. 32RE Ch. 1 - Prob. 33RE Ch. 1 - Prob. 34RE Ch. 1 - Prob. 35RE Ch. 1 - Prob. 36RE Ch. 1 - Prob. 37RE Ch. 1 - Prob. 38RE Ch. 1 - Prob. 39RE Ch. 1 - Prob. 40RE Ch. 1 - Prob. 41RE Ch. 1 - Prob. 42RE Ch. 1 - Prob. 43RE Ch. 1 - Prob. 44RE Ch. 1 - Prob. 45RE Ch. 1 - Prob. 46RE Ch. 1 - Prob. 47RE Ch. 1 - 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