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

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

Statement I Integral of an even function is not always an odd function. Statement II Integral of an odd function is an even function .

Left hand derivative and right hand derivative of a function f(x) at a point x=a are defined as f'(a^-)=lim_(hrarr0^(+))(f(a)-f(a-h))/(h) =lim_(hrarr0^(+))(f(a+h)-f(a))/(h) andf'(a^(+))=lim_(hrarr0^(+))(f(a+h)-f(a))/(h) =lim_(hrarr0^(+))(f(a)-f(a+h))/(h) =lim_(hrarr0^(+)) (f(a)-f(x))/(a-x) respectively. Let f be a twice differentiable function. We also know that derivative of a even function is odd function and derivative of an odd function is even function. If f is even function, which of the following is right hand derivative of f' at x=a?

Statement-1: Every function can be uniquely expressed as the sum of an even function and an odd function. Statement-2: The set of values of parameter a for which the functions f(x) defined as f(x)=tan(sinx)+[(x^(2))/(a)] on the set [-3,3] is an odd function is , (9,oo)

The function f(x)=(x+1)/(x^3+1) can be written as the sum of an even function g(x) and an odd function h(x) . Then the value of |g(0)| is___________

The function f(x)=(x+1)/(x^3+1) can be written as the sum of an even function g(x) and an odd function h(x) . Then the value of |g(0)| is___________

Which of the following functions is an odd function:

Which of the following functions is an odd function?

Statement-1: The function f(x) given by f(x)=sin^(-1){log(x+sqrt(x^(2)+1))} is an odd function. Statement:2 The composition of two odd functions is an odd function.

Let f (x)=|x-2|+|x - 3|+|x-4| and g(x) = f(x+1) . Then 1. g(x) is an even function 2. g(x) is an odd function 3. g(x) is neither even nor odd 4. g(x) is periodic