So we solved a question in class today:
Find the range of .
The general method we're told to follow is to find the inverse of the function and then find the domain of the inverse, which is the range of the function. So this was the solution put up.
Domain of will be . Let
Hence the range of is .
I argued that for , and hence should be a part of the range. But then my teacher told me that won't be a part of the range, as is not allowed in equation . But then I showed the teacher the definition of the range given in my textbook (NCERT), and it was the definition for the range of a relation. He said that the definition of a range is different for relations and different for functions.
Is he wrong or right? If he's wrong, how do I prove him wrong, and if he's right, what did I do wrong?
Wikipedia defines the range of a function as the image of the function, which makes me think that I'm right. Also, the graph of passes through the origin.