Yes. The domain and range can include Irrational Numbers.
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The domain is the possible values that can be input into the function and produce a real number output.
In algebra, the domain consists of all possible values for the x variable that could make the function work. The range is all of the possible values of the function, using each number in the domain.
An irrational number.
When added to a rational number, any irrational number will produce an irrational number.also, when added to an irrational number, any rational number will produce an irrational number.
It is not an irrational number!