Statement 1: If `f(x)` is an odd function, then `f^(prime)(x)` is an even function. Statement 2: If `f^(prime)(x)` is an even function, then `f(x)` is an odd function.

If f(t) is an odd function,then varphi(x)=int_(a)^(x)f(t)dt is an even function.

If f(x) is an odd function,then write whether f'(x) is even or odd.

If f(x) is an odd function, then the curve y=f(x) is symmetric

If f(x) is an even function,then write whether f'(x) is even or odd.

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

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and g(x)=f'(x) is an even function , then f(x) is an odd function.

Statement-1 : f(x) is a one-one function hArr f^(-1) (x) is a one-one function. and Statement-2 f^(-1)(x) is the reflection of the function f(x) with respect to y = x.

If f is an odd function and g is an even function,then fog is

Statement -1 : Integral of an even function is not always on odd function. Statement-2: Integral 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 .