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.

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

Statement - I : If f(x) is an odd function, then f'(x) is an even function. Statement - II : If f'(x) is an even function, then f(x) is an odd function.

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

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

If f(z) is an odd function, prove that, int_(a)^(x)f(z)dz is an even function.

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

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

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

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