Question

Hey, I'm stumped on how to determine the correct domain for the problem, I attached the first ss of the two functions, the second ss is my own work. I would really appreciate if someone could show me where I went wrong with the domain.

Answer 1

I appreciate that you've shown your work.

It turns out that you're on the right track, and you have the correct final function. However, the domain isn't correct.

x = 2 is not allowed in the domain even though the (x-2) portions do indeed cancel out.

The reason why x = 2 isn't allowed is because f(2) isn't defined.

Therefore the domain should be "set of all real numbers except x = -3, x = 2, x = 3" or we could say "set of all real numbers but x ≠ -3, x ≠ 2, and x ≠ 3"

The interval notation for the domain would be:

(-∞, -3) U (-3, 2) U (2, 3) U (3, ∞)

This is basically us poking holes at x = -3, x = 2, and x = 3 on the real number line to exclude those values. Anything else works in the domain.