Is there a function f which is both even and 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? G(x) is an odd function G(x)i s an even function G(x) is neither even nor odd function. Whether G(x) is an odd or even function depends on the value of a

If f:[0,2pi]vec[-1,1]; y=sin x then which of statement is/are true: y=f^(-1)(x) is an odd function y=f^(-1)(x)-pi is an odd function y=f^(-1)(x) is an even function y=f^(-1)(x) is neither even nor odd function

Let f (x)=|x-2|+|x - 3|+|x-4| and g(x) = f(x+1) . Then 1. g(x) is an even function 2. g(x) is an odd function 3. g(x) is neither even nor odd 4. g(x) is periodic

If f : R - R is an even function which is twice differentiable on R and f''(pi)=1 , then f''(-pi)

Find whether the following function is even or odd: f(x) = x tan^3x + x^(3)"cosec" x

Determine whether the function is even, odd or niether even or odd. (a) f(x)=5-x^(2) (b) f(x)=|-x| (c ) f(x)=[x] (d) f(x)=|x-2| (e) f(x)=-x|x|

Let f(x) be real valued and differentiable function on R such that f(x+y)=(f(x)+f(y))/(1-f(x)dotf(y)) f(x) is Odd function Even function Odd and even function simultaneously Neither even nor odd

Statement I Integral of an even function is not always an odd function. Statement II Integral of an odd function is an even function .

The function f(x)=log(x+sqrt(x^(2)+1)) , is (a) an even function (b) an odd function (c ) a periodic function (d) Neither an even nor an odd function.