The domain of a function is the set of all possible inputs or, in other words, the set of all inputs for which the given function is defined.

If we are talking about real-valued functions the typical domain is all real numbers. There are times when a function could have a more restrictive domain.

For example we cannot divide by zero. Any value for the independent variable that causes a division by zero is not in the domain. So if f(x) = 1/x the domain is all real numbers except zero. If `f(x) = 1/((x+2)(x-3))` then the domain is all real numbers except -2 and 3.

Another example is that we cannot take an even-indexed root of a negative number in the reals because the result is an imaginary number. So if `f(x) = sqrt(x)` the domain is `x> = 0` . If `f(x) = root[4](-2x-4)` then the domain is `x< = -2`

We also cannot take logarithms of negative inputs. Thus f(x) = ln(x) has a domain of x>0.

**We are given d(x) = -7500+80x. As a mathematical function the domain is all real numbers. However there is another consideration.**

We often use mathematical functions to model a physical situation. In these cases there are other possible restrictions on the domain. In geometry lengths must be nonnegative; no human is taller than 10 feet tall, so any function modeling human characteristics cannot use an input height that large, for example. Also, the model may only match reality over a particular time period.

So is d(x) a model for some situation (depth, existing debt, etc.)? If so, there may be some constraints. Perhaps the variable cannot be negative, or has some largest value, or is restricted to integers. If d(x) represents a model, you will want to list the limitations as restrictions on the domain.

**Further Reading**