Final answer:
To define (f + g)(x) with the given functions f(x) = 5 / (x + 12) and g(x) = x - 3 + 10, we add them together to get (5 / (x + 12)) + (x + 7).
Step-by-step explanation:
When asked which function defines (f + g)(x), with f(x) = 5 / (x + 12) and g(x) = x - 3 + 10, we simply need to add the two functions together. The function (f + g)(x) is found by adding f(x) and g(x) algebraically, which is (5 / (x + 12)) + (x + 7). Thus, the combined function (f + g)(x) is a new function that can be simplified if necessary.
To demonstrate addition of functions using variables, consider f(x) and g(x) as separate expressions, add them together, and combine like terms. In this case, there aren't any like terms besides the constant from g(x) added to the rational function from f(x).