What is the domain of the function f(x) = 2x^2 - 3?

Domain: Set of all real numbers

If you want to express the domain in set-builder notation, then you'd write something like  which is fancy notation to basically say "x is any real number"

If you want to write the domain in interval notation, then you'd write  which is the interval from negative infinity to positive infinity. In other words, the entire real number line.

-----------------------------------------------------------------

The domain is the set of all real numbers because we don't have any restrictions to worry about. There are no division by zero errors. There are no cases where we have to worry about taking the square root of a negative number, or anything similar. Any number can replace x to generate an output for y.