Question

If f(x)=x+7 and g(x)=1/x-13, what is the domain of (f o g) (x)?

Answer 1

There’s an ambiguity in g(x): it could mean (1/x) − 13 or 1/(x − 13). For both cases the composite is f(g(x)) = g(x) + 7, and since f has domain all reals the only restrictions come from where g is undefined.

- If g(x) = 1/x − 13, then f∘g(x) = 1/x − 6, so domain: all real x with x ≠ 0.
- If g(x) = 1/(x − 13), then f∘g(x) = 1/(x − 13) + 7, so domain: all real x with x ≠ 13.