Range of function always a subset of its domain?

I have a question regarding functions. For a function with a pre-defined domain, would the corresponding range always be a subset of this domain?

Student X

This is not necessarily true. For example, consider f(x) = (2x -1)/(x-5), where the domain is defined to be the set of all real values of x except for x=5 (since it is an asymptotic value). Based on this, the range is therefore given as negative infinity to infinity aka the set of real values excluding y=2. This clearly demonstrates that the range of a function need not always be a subset of the domain of the same function.

Hope this helps. Peace.

Best Regards,

Mr Koh