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) be an even function. Then f'(x)

If f(x) is an odd function then int_(-a)^(a)f(x)dx is …………. .

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

The product of an odd function and an even function is:

Let f:(-pi/2,pi/2)vecR be given by f(x)=(log(sec"x"+tan"x"))^3 then a) f(x) is an odd function b) f(x) is a one-one function c) f(x) is an onto function d) f(x) is an even function

Let f: R->R be a differentiable function for all values of x and has the property that f(x)a n df^(prime)(x) has opposite signs for all value of xdot Then, (a) f(x) is an increasing function (b) f(x) is an decreasing function (c) f^2(x) is an decreasing function (d) |f(x)| is an increasing function

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then f(x) is an increasing function in (0,oo) f(x) is a decreasing function in (-oo,oo) f(x) is an increasing function in (-oo,oo) f(x) is a decreasing function in (-oo,0)

Statement 1 : For a continuous surjective function f: RvecR ,f(x) can never be a periodic function. Statement 2: For a surjective function f: RvecR ,f(x) to be periodic, it should necessarily be a discontinuous function.

Let f(x) be and even function in R. If f(x) is monotonically increasing in [2, 6], then