Domain and Range/Codomain of a Composite Function

The domain and range of a composite function can often be deduced from the functions of which which that function is composed.
The domain of  
  is the domain of  
  and the range of  
  is restricted to  
\[f(Range \: of \: g(x))\]
  is the composition  
  of the two functions  
The domain of  
  (and of  
) is  
\[x \ge 1\]
  and the range is the set of values taken by  
\[x \ge 0\]
  i.e. the range is  
\[y \ge 1\]

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