The domain of a piecewise defined function can be both implied and explicitly described, depending on how the function is defined.
When a piecewise function is introduced, it often consists of multiple expressions valid for different intervals of the input variable. The parts of the function usually include conditions that indicate the interval or condition under which each expression applies. These conditions help specify the limitations on the domain.
For example, consider the piecewise function:
f(x) = { x^2, if x < 0
{ x + 1, if x >= 0
In this case, the domain is explicitly defined because the function states the conditions (x < 0 and x >= 0) that dictate which expression to use. However, if these conditions were not provided, it might only be implied that the function is defined for all real numbers, although a complete understanding would require further context.
In summary, while a piecewise defined function’s domain can be clearly laid out in its definition, it can also be inferred through context or conventions. Always ensure that the conditions are visible to avoid confusion about the function’s domain.