If 𝑓 is a function from the set 𝑋 to the set 𝑌, what do we call 𝑋?
Remember, a function is a special type of relation or mapping that maps elements from one set onto exactly one element in the second set. In this case, our function 𝑓 maps elements from the set 𝑋 to the set 𝑌. If we say that lowercase 𝑥 is some element of set 𝑋 and lowercase 𝑦 is some element in set 𝑌, then we can represent this by saying 𝑦 is equal to 𝑓 of 𝑥; 𝑦 is some function of 𝑥. And when we think about functions, there are two special words we use to describe the relevant sets.
The elements in set 𝑋 , which we’ve defined to be lowercase 𝑥, are all possible inputs to the function. And the elements in set 𝑌, which we’ve defined to be lowercase 𝑦, are all possible outputs. And when we think about the set of possible inputs of a function, we’re thinking about the domain of the function, whilst when we think about the set of possible outputs, we’re thinking about its range.
The question asks us here “what do we call 𝑋?” Since 𝑋 is the set of possible inputs for our function 𝑓, then 𝑋 is the domain of the function.