I presented the following example in my Precalculus classes this past week and it bothered students:
Let and . Compute and and state the domain of each.
As usual, I’ll give you a second to think about it yourself.
Here are the answers:
The reason that the first one was unsettling, I think, is because of the restricted domain (despite the fact that the simplified form of the answer seems not to imply any restrictions).
The reason the second one was unsettling is because they had forgotten that . It seems to be a point lost on many Algebra 2 students.