To prove: product of two odd functions is an even function and the product of two even function is an even function
Explanation of Solution
Concept Used:
A function
A function
First prove that product of two odd functions is an even function.
Let
Then,
And
Now, consider the product of these two odd functions.
Now check if this function is even or odd.
By definition, clearly
Thus, product of two odd functions is an even function.
Now prove that product of two even functions is an even function.
Let
Then,
And
Now, consider the product of these two even functions.
Now check if this function is even or odd.
By definition, clearly
Thus, product of two even functions is an even function.
Chapter 1 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning