Question

What is the domain and range of `(3x^2)/(x^2-4)`?

Answer 1

The Domain is any real number except 2 or -2.
The Range is any real number.

Explanation:

Domain

`(3x^2)/(x^2 -4) = (3x^2)/((x+2) (x-2))`

This means x cannot be 2 or -2, since the denominator would be 0, making the expression undefined, so the domain is any real number except 2 or -2.

Range

For this you have to take the limit as x approaches 2 from the positive and negative sides. Same with -2. That's 4 separate limits, 2 of which approach positive infinity, the other 2 negative infinity. So the range includes all real numbers.