please find the domain

edited

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## 1 Answer

Do I read this as f of g, where f(x)=5/(x-4), g(x)=1/x? First, look at the domain of each function separately. g(x)=1/x (if this isn't quite what was in the original question you were given before you submitted it, it looks like it contained a term involving dividing by x). The domain is the scope of values of the subject of the function, in this case x. We cannot divide by zero so the domain of x in g is every value of x except x=0, where g becomes infinite and can't be defined. When we put g(x) as the subject of f we have 5/(g(x)-4). That's f of g or "fog". As long as g(x) isn't 4, f is defined, but when g(x)=4, f doesn't exist (infinity can't be defined). What value of x would make g(x)=4? If g(x)=1/x, then 4=1/x, so x=1/4. We've found two values of x that can't be used, so the domain of fog is x not equal to zero and x not equal to 1/4. Hope this helps.

by Top Rated User (906k points)
thanks and yes it did help.....

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