Hi Hok, just had a doubt. If say we needed to find the domain of sin(ArcTan (x)) , I constructed the domain and range table and found that the range of the inner function arctan x is a subset of the range of outer function sinx. Which is (-Pi/2, Pi/2) ,compared to [-Pi/2,Pi/2]. So in this case do we say the domain implied is x E R?

I don't get why implied domain is domain of g(x) and implied range is range of f(x)