Find the domain and the range of each of the following real function:

Given:

Need to find: Where the functions are defined.

The condition for the function to be defined,

⇒

So, the domain of the function is the set of all the real numbers lesser than 3.

The domain of the function, D_f(x) = (-∞, 3).

The condition for the range of the function to be defined,

&

⇒ &

Both the conditions can’t be satisfied simultaneously. That means there is no range for the function f(x).