Closed 7 years ago. I understand some of the basic concepts that surrounds even and odd functions but this question just stumped me and I'm not sure on how to tackle it. Any Starting …

The sum of an even function and an odd function maybe even, odd, both, or neither. Bear in mind that the constant 0 function is both even and odd, as that should help you construct explicit …

While working on a proof showing that all functions limited to the domain of real numbers can be expressed as a sum of their odd and even components, I stumbled into a troublesome …

A function from the real numbers to the real numbers is is a rule that assigns to each real number $x$ another number, which we write as $f (x)$. So it doesn't make sense to talk about the …

9 I need to show that $f (x) = \log (x + \sqrt {x^2+1})$ is an odd function and from what I can understand from this question (found while searching): What is an odd function?, I have to …

There are many reasons why we call those even and odd functions. One is that the taylor series of an even function only includes even powers whereas the Taylor series of an odd function …

b) A function $g$ is even if it is defined on a symmetric interval around zero , that is $ [-a, a]$ and $f (-x)=f (x)$. Now, consider the functions you want to study whether they are even or odd as …

Definite integral of even and odd functions proof Ask Question Asked 9 years ago Modified 9 years ago

Odd function means rotational symmetric, if you rotate an arrow, I.e. direction, you will change by 180 degree, so it is the same slope, hence the derivative of odd function is even.

That can be rephrased as "if' is odd then f is even and if f' is even then f is odd". Since integration is the inverse operation to differentiation, replacing f' with f and r with $\int f dx$ " we have "if f …