Question

The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except of -3. What is the domain of (g*f)(x)?

Answer 1

all real numbers except 7 and -3

Explanation:

when you multiply two functions, what are we doing?
we are taking the f(x) value and multiply it by the g(x) value, where x must be the same. However both functions have restrictions, 7 and -3, so the product of the two functions, must have * both * restrictions.

Usually when having operations on functions, if the previous functions (`f(x) and g(x)`) had restrictions, they are always taken as part of the new restriction of the new function, or their operation.

You can also visualize this by making two rational functions with different restricted values, then multiply them and see where the restricted axis would be.