If `f(x) =x/(e^x-1)+x/2+1 and g(x) =min {|x-1|,|x|,|x+1|},` then

If function f(x)=x^(2)+e^(x//2) " and " g(x)=f^(-1)(x) , then the value of g'(1) is

If the function f(x) = x^3 + e^(x/2) and g(x) =f^-1(x) , then the value of g'(1) is

If the function f(x)=x^(3)+e^((x)/(2)) and g(x)=f^(-1)(x) , then the value of g'(1) is

If function f(x)=x^(2)+e^(x//2) " and " g(x)=f^(-1)(x) , then the value of g'(x) is

Let f(x) = (e^(x) - e^(-x))/(2) and if g(f(x)) = x , then g((e^(1002) -1)/(2e^(501))) equals ...........

Let f(x) = (e^(x) - e^(-x))/(2) and if g(f(x)) = x , then g((e^(1002) -1)/(2e^(501))) equals ...........

If the function f(x)= x^(3)+e^(x/2) and g(x) = f^(-1)(x) then the value of g^(')(1) is

Let f(x){sin pix , 0 le x le 2 and 2-x, 2 < x le 5, g(x) ={max(|x|, 1-|x|,|x-1|) if x in (0,1) and min(|x|, 1-|x|,|x-1|) otherwise. Then find f(g(x)).