Given `f(x)=sqrt(x-2),g(x)=1/x` find the domain of `(g circ f)(x)` :

The domain of the composite function is the set of all x such that x is in the domain of f(x) and f(x) is in the domain of g(x).

The domain of f(x) is `x>=2` (assuming f(x) is a real-valued function) and the domain of g(x) is `x != 0` .

The domain of `g(f(x))` is all x in the domain of f(x) so `x>=2` such that f(x) is in the domain of g(x). So `sqrt(x-2)!=0 ==> x-2!=0 ==> x!=2`

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The domain of g(f(x))is x>2

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`g(f(x))=1/sqrt(x-2)` : the graph:

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