`text(Definitions)`

Let `f(x)` and `g(x)` be two real valued functions.

The sum of two functions is denoted by `(f + g)(x)` and is equal to `f(x) + g(x).`

The difference of two functions is denoted by `(f - g)(x)` and is equal to `f(x) - g(x).`

The product of two functions is denoted by `(fg)(x)` and is equal to `f(x)g(x).`

The quotient of two functions is denoted by `(f/g) (x)` and is equal to `f(x)/g(x)` as long as `g(x) ne0`

The domain of each of these combinations is the intersection of the domain of `f` and the domain of `g.` In other words, both functions must be defined at a point for the combination to be defined. One additional requirement for the division of functions is that the denominator can't be zero, but we knew that because it's part of the implied domain.