Video: Determining the Domain of Piecewise-Defined Functions

Find the domain of the real function 𝑓(π‘₯) = 6π‘₯ if 15< π‘₯< 20 and 𝑓(π‘₯) = 6 βˆ’ π‘₯ if 20 ≀ π‘₯< 50.

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Video Transcript

Find the domain of the real function 𝑓 of π‘₯ equals six π‘₯ if π‘₯ is between 15 and 20. 𝑓 of π‘₯ equals six minus π‘₯ if π‘₯ is greater than or equal to 20 but less than 50.

The domain of a function, the set of all possible independent values, all possible π‘₯ values, the place where the function exists. First, we’re told that π‘₯ exists between 15 and 20. π‘₯ is greater than 15, but not equal to 15. So we say that π‘₯ is greater than 15. The bracket faces outward because π‘₯ cannot be equal to 15.

Our next piece of the function tells us that π‘₯ exists if it’s equal to or greater than 20 but less than 50. Because the breaking point for the piecewise function includes 20, there are no holes in this function. There are possible values for π‘₯ all the way up to 50, but not including 50. There is an outcome for every π‘₯ value between 15 and 50, but not including 15 and 50.

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