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^(prime)(x) is even or odd.

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

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

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

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(t) is an odd function, then prove that varphi(x)=int_a^xf(t)dt is an even function.

If f is an even function, then prove that lim_(x->0^-) f(x) = lim_(x->0^+) f(x)

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

If f(x) is an even function then find the number of distinct real numbers x such that f(x)=f((x+1)/(x+2)).