Odd function times odd function

The product of two odd functions is an even function.

1. Why is the sum of two odd functions odd?
2. Do odd functions have odd powers?
3. Is the product of two even functions even?
4. Is every odd function one to one?

Why is the sum of two odd functions odd?

Example: Sum Of Two Odd Functions

Let f(x) = x³ + 2x and g(x) = x⁷ + 4x⁵. Both f(x) and g(x) are odd functions, since they are polynomials whose terms have odd powers of x. The graph of the odd function f(x) = x³ + 2x.

Do odd functions have odd powers?

Odd Function Example

The graph looks symmetrical about the origin. Note that all functions having odd power like are odd functions. f(x) = x⁷ is an odd function but f(x) = x³ + 2 is not an odd function.

Is the product of two even functions even?

The product of two even functions is even, the product of two odd functions is even, and the product of an odd function and an even function is odd. Let f and g be functions on the same domain, and assume that each function takes at least one non-zero value.

Is every odd function one to one?

An odd function can be one-to-one. However, not every odd function is one-to-one. For example, f(x) = x is an odd function, and it is one-to-one (it passes the horizontal line test).