![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_largeCoverImage.gif)
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
- a. A function could have the property that f(−x) = f(x), for all x.
- b. cos (a + b) = cos a + cos b, for all a and b in [0, 2π].
- c. If f is a linear function of the form f(x) = mx + b, then f(u + v) = f(u) + f(v), for all u and v.
- d. The function f(x) = 1 − x has the property that f(f(x)) = x.
- e. The set {x: |x + 3| > 4} can be drawn on the number line without lifting your pencil.
- f. log10(xy) = (log10 x)(log10 y)
- g. sin−1 (sin (2π)) = 0
a.
![Check Mark](/static/check-mark.png)
Whether the given statement is true and give an explanation or a counter example.
Answer to Problem 1RE
The given statement is true.
Explanation of Solution
Given:
The given statement is “A function could have a property that
Calculation:
Consider the function
Now, check whether the above mentioned function satisfies the property
Therefore, the statement is true.
b.
![Check Mark](/static/check-mark.png)
Whether the given statement is true and give an explanation or a counter example.
Answer to Problem 1RE
The statement is false.
Explanation of Solution
Given:
The given identity is “
Calculation:
Take
Similarly, calculate the right hand side of the identity as follows.
That is,
Therefore, the statement is false.
c.
![Check Mark](/static/check-mark.png)
Whether the given statement is true and give an explanation or a counter example.
Answer to Problem 1RE
The statement is false.
Explanation of Solution
Given:
The given statement is “If
Calculation:
Take
The right hand side of equation
And, the left hand side of equation
Thus,
Therefore, the statement is false.
d.
![Check Mark](/static/check-mark.png)
Whether the given statement is true and give an explanation or a counter example.
Answer to Problem 1RE
The statement is true.
Explanation of Solution
Given:
The given statement is “The function
Calculation:
Consider the function
Calculate
Therefore, the statement is true.
e.
![Check Mark](/static/check-mark.png)
Whether the given statement is true and give an explanation or a counter example.
Answer to Problem 1RE
The statement is false.
Explanation of Solution
Given:
The given statement is “The set
Calculation:
The given set
Therefore, the set
Therefore, the statement is false.
f.
![Check Mark](/static/check-mark.png)
Whether the given statement is true and give an explanation or a counter example.
Answer to Problem 1RE
The statement is false.
Explanation of Solution
Given:
The given statement is “The equation,
Calculation:
Take,
Similarly, calculate the right hand side of the equation as shown below.
Then,
Therefore, the statement is false.
g.
![Check Mark](/static/check-mark.png)
Whether the given statement is true and give an explanation or a counter example.
Answer to Problem 1RE
The statement is true.
Explanation of Solution
Given:
The given statement is “The equation,
Calculation:
Consider
Then, compute the following.
Thus,
Therefore, the statement is true.
Want to see more full solutions like this?
Chapter 1 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Precalculus
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- Determine whether each of the following statements is true or false, and explain why. The only function that is its own derivative is ex.arrow_forwardDetermine whether each of the following statements is true or false, and explain why. The chain rule is used to take the derivative of a product of functions.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
![Text book image](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781680331141/9781680331141_smallCoverImage.jpg)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780395977224/9780395977224_smallCoverImage.gif)