assume that s is an odd function and t is an even function, and both s and t are defined on the entire real line |R .. are the following functions odd or even..
I. st II. s/t III. s°t ???

Question

assume that s is an odd function and t is an even function, and both s and t are defined on the entire real line |R .. are the following functions odd or even..
I.  st     II.  s/t      III.  s°t                ???

anonymous · Answer

An odd function is a function for which f(-x) = -f(x), and an even function is a function for which f(-x) = f(x) for all x in the domain of f.

The sum of an even and odd function is neither even nor odd, unless one of the functions is equal to zero over the given domain.
The sum of two even functions is even, and any constant multiple of an even function is even.
The sum of two odd functions is odd, and any constant multiple of an odd function is odd.
The product of two even functions is an even function.
The product of two odd functions is an even function.
The product of an even function and an odd function is an odd function.
The quotient of two even functions is an even function.
The quotient of two odd functions is an even function.
The quotient of an even function and an odd function is an odd function.
The composition of two even functions is even, and the composition of two odd functions is odd.
The composition of an even function and an odd function is even.
The composition of any function with an even function is even (but not vice versa).

anonymous · Answer

thaaaaaaaaaanksssss aloot for the helpful details!!