Odd and Even Extension | Equal function

Odd and Even Numbers

Let f(x) = e^x + sin x be defined on the interval [–4, 0]. Find the odd and even extension of f(x) in the interval [–4, 4].

Let f(x)=x^(2)+x be defined on the interval [0,2). Find the odd and even extensions of f(x) in the interval [-2,2] .

Odd & Even Function

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

log(x-3) is (A) is an even function (B) an odd function (C) neither even nor odd (D) cannot be determined

Prove that the product of two even or two odd functions is an even function, whereas the product of an even and an odd function is 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

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