If `f(x) = sqrt(x)+1/(sqrt(x))` find , the value of 2xf'(x) + f(x).

If f (x) =x^3-1/x^3 , find the value of f (x) +f (1/x) .

If f (x) = cos (log_e x) , find the value of : f(x) f(y)-1/2[f(x/y)+f(xy)] .

Let f(x)= (sqrt(x+3))/(x+1) , then the value of lim_(x rarr -3^-) f(x) is :

f(x)=sqrt(2-abs(x))+sqrt(1+abs(x)) . Find the domain of f(x).

f(x)=sqrt(x^(2)-abs(x)-2) . Find the domain of f(x).

If f(x) = (sqrt(2) cos x-1)/(cotx-1) , x nepi/4 , find the value of f(pi/4) so that f(x) becomes continuous at x = pi/4

If f(x)=sqrt(x+2sqrt(2x-4))+sqrt(x-2sqrt(2x-4)) then the value of 10 f'(102^(+)) , is

Let f(x) = sqrt(1-sqrt(1-x^2) then f(x) is

f(x)=sqrt((log(x-1))/(x^(2)-2x-8)) . Find the domain of f(x).