To Check : whether h is necessarily even function if
Answer to Problem 70E
Function h is necessarily even, if g is even. If g is odd, the nature of h depends on f. If both g and f are odd, h is odd. If g is odd and f is even, h is even.
Explanation of Solution
Given information : Given
Formula used : The concept of Composition of Functions and Odd/ Even Functions is used.
Calculation :
In part 1, g is even function
So, for h to be even function
And
Thus, h is necessarily even function, if g is even function.
In part 2, g is odd function
So, for h to be even function
Thus, as the nature of f is not known, we can’t say whether h is even or odd.
In part 3, g is odd function and f is odd
So, for h to be even function
Thus, h is an odd function, if g is odd function and f is odd function.
In part 4, g is odd function and f is even
So, for h to be even function
Thus, h is a even function, if g is odd function and f is even function.
Chapter 2 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- 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