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

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.

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

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.

if f is an increasing function and g is a decreasing function on an interval I such that fog exists then

Odd & Even Function

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1+x) then (1) g(x) is an odd function (2)g(x) is an even function (3) graph of f(x) is symmetrical about the line x=1 (4) f'(1)=0

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

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