How do you determine if x/(x^2 -1) is an even or odd function?

1 Answer
Jul 28, 2016

x/(x^2-1) is an odd function

Explanation:

  • An even function is one for which f(-x) = f(x) for all x in the domain.

  • An odd function is one for which f(-x) = -f(x) for all x in the domain.

In our example:

f(x) = x/(x^2-1)

f(-x) = (-x)/((-x)^2-1) = (-x)/(x^2-1) = -x/(x^2-1) = -f(x)

So x/(x^2-1) is an odd function.

graph{x/(x^2-1) [-10, 10, -5, 5]}