If c(x)=5/x-2 and d(x)=x+3 what is the domain of (cd)(x)?

First you must realize that the domain is restricted for c(x), in that division by zero is undefined, so x cannot equal 2.  Realizing this before you start is important because the final form of (cd)(x) may appear to not have that restriction, but having x=2, would still have no meaning regardless of what (cd)(x) becomes.

(cd)(x)=5(x+3)/(x-2)

(cd)(x)=(5x+15)/(x-2)

Now we can see that the same restriction applies to the composite function, so the domain is:  x=(-oo, 2)U(2, +oo).  "All real numbers except two."

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