Question

Is it possible for an odd function to have the interval 0 infinity) as its domain?

Answer 1

Answer with Step-by-step explanation:

Yes, it is possible for an odd function to have the interval 0 to infinity as its domain.

Let f(x) = -x

f(-x)= -(-x)

     = x

and -f(x)= -(-x)

            = x

Clearly, f(-x) = -f(x)

Hence, f(x) = -x  is an odd function.

and clearly the domain of f(x) = -x is the set of all real numbers which also contains the interval (0,∞)

Hence, it is possible for an odd function to have the interval 0 to infinity as its domain.

Answer 2

NO!

Prove by contradiction. First, define the the following terms:

odd function: f(-x) = -f(x)] and domain: all values of x

Proof: Suppose there f(-x) = -f(x) such that x is a negative integer, then f(-x) is a positive number (-(-x) = +x) and -f(x) is a negative number (negative of a positive number is a negative number). Since a positive number cannot equal a negative number, then this is not possible.

Answer: No