To determine algebraically whether a function is odd, substitute
-x into the and simplify. If the resulting is equal to
-f(x), then the function is odd; otherwise, it is not. For example, consider the following function.
f(x)=x2−1x
Substitute
-x for
x and simplify.
f(x)=x2−1x
f(-x)=(-x)2−1-x
f(-x)=x2−1-x
f(-x)=-x2−1x
f(-x)=-f(x)
Since
f(-x)=-f(x), the given function is odd.