Properties of odd and even function

Odd & Even Function

Let f(x)=e^(e^(|x|sgnx))a n dg(x)=e^(e^(|x|sgnx)),x in R , where { } and [ ] denote the fractional and integral part functions, respectively. Also, h(x)=log(f(x))+log(g(x))dot Then for real x , h(x) is (a)an odd function (b)an even function (c)neither an odd nor an even function (d)both odd and even function

Prove that the derivative of an even function is an odd function and that of an odd function is an even function.

The derivative of an even function is always an odd function.

Let f(x) be real valued and differentiable function on R such that f(x+y)=(f(x)+f(y))/(1-f(x)*f(y))f(x) is Odd function Even function Odd and even function simultaneously Neither even nor odd

Prove that sum of odd and even is odd.

Properties OF Even & Odd function & Illustration

Definite Integration Of Odd And Even Functions

Let G(x)=(1/(a^x-1)+1/2)F(x), where a is a positive real number not equal to 1 and f(x) is an odd function. Which of the following statements is true? (a)G(x) is an odd function (b)G(x)i s an even function (c)G(x) is neither even nor odd function. (d)Whether G(x) is an odd or even function depends on the value of a