`f(x) = sgn (x) + x^2` Determine, whether even or odd function

Determine whether even or odd: f(x)=x((a^x+1)/(a^x-1))

If f(x)=x.log((1-x)/(1+x)), determine whether the function f is even or odd or neither.

The function f(x) = tan(x)^(11)e^(x^5)sgn(x^(11)).[1/(3x^2+2)] , where [.] denotes greatest integer function , is a)even function b)odd function c)even as well as odd function d)neither even nor odd function

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

Determine whether the functions are even or odd f(x)=abs(x-2)

Determine whether the functions are even or odd f(x)=abs(-x)

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

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.

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