Functions, the compositions of f(g(x))

  • Thread starter Thread starter CrossFit415
  • Start date Start date
  • Tags Tags
    Functions
AI Thread Summary
If both functions f(x) and g(x) are odd, their composition f(g(x)) is also an odd function. This is because the property of odd functions, where f(-x) = -f(x), holds through the composition. By substituting -x into the composition, it can be shown that f(g(-x)) equals -f(g(x)). Therefore, the correct answer to the homework statement is that the composition is always an odd function. Understanding the properties of odd functions is key to solving such problems.
CrossFit415
Messages
160
Reaction score
0

Homework Statement



Suppose two functions f(x) and g(x) are both odd functions. Then, their composition f(g(x)) is;

Homework Equations



A. Always an odd function

B. Always an even function

C. Sometimes an even function, and sometimes an odd function

D. None of the above

The Attempt at a Solution



What numbers do I plug in? How do determine which are the odd functions?
 
Last edited:
Physics news on Phys.org
Hi CrossFit415! :smile:

CrossFit415 said:
What numbers do I plug in? How do determine which are the odd functions?

Just start "f(g(-x)) = … " :wink:
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
Back
Top