Q2:

What are the domain and range of f  where ?

and what about  ?

 

A2:

The definition of  f specifies a result for all real numbers x except 0.  

So, using  for the domain of f, we can say that .

And the result is always either 1 or -1, so the range of f is just the set consisting of just these two numbers  which we can write in set notation as .

 

 

But what was given as the “definition” of g specifies two different outputs for , so does not define a function.