Let `g: Rrarr(0,pi/3)` be defined by `g(x)=cos^(-1)((x^2-k)/(1+x^2))` . Then find the possible values of `k` for which `g` is a surjective function.

Let g:[1,3]rarrY be a function defined as g(x)=In(x^2+3x+1) .Then find g^(-1)(x) if it exist.

Let g:[1,3]rarrY be a function defined as g(x)=In(x^2+3x+1) .Then Find the set of Y so that g(x)in onto.

Let g(x) be the inverse of f(x) and f'(x)=1/(1+x^3) . Then find g'(x) in terms of g(x).

Let f:R->[1,oo) be defined as f(x)=log_10(sqrt(3x^2-4x+k+1)+10) If f(x) is surjective then k =

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

Let g:[1,3]rarrY bae a function defined as g(x)=In(x^2+3x+1) .Then Determine whether g(x) is one -one or many one.

Let f(x)=(1)/(1+x^(2)) and g(x) is the inverse of f(x) ,then find g(x)

Let g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0. then the value of 8g(pi/2) is __________

Let the function f : R to R , g : R to R , h : R to R be defined by f(x) = cos x,g(x) = 2x+1 and h(x) = x^(3)-x-6 , Find the mapping h o (go h) , hence find the value of h o (go f), hence find the value of ( h o (go f) ) (x) when x=(pi)/(3) and c=(2pi)/(3).

Let f and g be two functions defined by f(x)=(x)/(x+1), g(x) =(x)/(1-x) . If ( f o g ) ^(-1) (x) is equal to kx, then find the value of k.