Definition, even odd function, Periodic function

Let f(x) be a continuous function in R such that f(x) does not vanish for all x in R . If int_1^5 f(x)dx=int_-1^5 f(x)dx , then in R, f(x) is (A) an even function (B) an odd function (C) a periodic function with period 5 (D) none of these

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.

The function 'g' defined by g(x)= sin(sin^(-1)sqrt({x}))+cos(sin^(-1)sqrt({x}))-1 (where {x} denotes the functional part function) is (1) an even function (2) a periodic function (3) an odd function (4) neither even nor odd

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

Even and Odd Function

Suppose that f is an even function, g is an odd function and both f and g are defined on the entire real line R. Which of the following wherever defined are odd function ?

Q.The function f(x)=ln[x^(3)+sqrt(x^(6)+1)] is an (a) even function (b) odd function (c) increasing function (d) decreasing function

Even And Odd Functions

Definite Integration Of Periodic Functions