The range for the given domain of the function f(x) =3x-6/x+4.5 is what

The domain is the input number values you can substitute into the equation.

The range is the output values how do they appear like, what is the nature of the numbers.

So for f(x) = 3x  -  6/x  + 4.5

You can input any real number value for x, except 0, because you can not divide by 0,  that is the 6/0.

So the domain is x set of all real numbers except 0.  R - {0}

So when we substitute any number into f(x) = 3x  -  6/x  + 4.5, what kind of numbers do we get?

We get Real numbers, 0 is included.

So the range for f(x) set of all real numbers.