If `g(x)=2tan^-1(e^x)-pi/2` is Even /odd

Let the function g:(-oo, oo) to (-(pi)/(2), (pi)/(2)) be given by g(u)=2tan^(-1)(e^(u))-(pi)/(2) . Then g is :

If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)-pi/2. Then, g is

If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)-pi/2. Then, g is

Let f(x)={x^(2)-4,quad if |x| and g(x)=2tan^(-1)(e^(x))-(pi)/(2) for all x in R, then which of the following is(are) correct?

If the function g:(-oo,oo)rarr(-(pi)/(2),(pi)/(2)) is given by g(u)=2tan^(-1)(e^(u))-(pi)/(2). Then g is

lim_(xtooo) (e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

lim_(xtooo) (e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

lim_(xtooo) (e^(1//x^(2))-1)/(2tan^(-1)(x^(2))-pi) is equal to

Determine whether the function f(x) = x((e^(x)-1)/(e^(x)+1)) is even or odd

If f(x)=2x+tan x and g(x) is the inverse of f(x) then value of g'((pi)/(2)+1) is