Show that `y = log(1 +x) - (2x)/(2 + 2x) , x gt -1`, is an increasing function of x throughout its domain.

The function f(x) = tan^(-1) (sin x + cos x), x gt 0 is always an increasing function on the interval

Show that the function f given by f(x) = tan^(-1) (sin x+cosx ) , x gt 0 is always an increasing function in (0,(pi)/(4)) .

Show that the function given by f (x) = e ^(2x) is increasing on R.

If y = log (x + sqrt(x^(2)+1) then dy/dx =

The value of f(0) so that the function f(x) = (2x-sin^(-1)x)/(2x+tan^(-1)x) is continuous at each point of its domain

If f(x)=sin ^(-1)(log _(2) (x^(2)/(2))) , then thedomain of the function is

The function f(x)=log(x+sqrt(x^(2)+1)) is :

The domain of the function cos ^(-1)(2 x-1) is

The domain of the function f(x)=sqrt(2-2x-x^2) is