continuous domain
a set of input values that consists of all numbers in an interval
The continuous domain refers to the set of all possible input values or independent variables in a mathematical function that can take on any real number. In other words, it is the range of values over which the function is defined and continuous without any gaps or discontinuities.
For example, the function f(x) = 2x + 1 has a continuous domain across all real numbers because we can plug any arbitrary real number into x, and the function will produce a corresponding output without interruption.
On the other hand, functions like f(x) = 1/x or f(x) = √x have a restricted domain, because they have values that result in a divide-by-zero error or square root of a negative number.
Therefore, we can say that a function has a continuous domain when there are no gaps or breaks in the function’s input values, and it is defined for all values of the independent variable.
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