Finding the Range

Question

I was having trouble finding the range of the equation and was wondering if this was correct.

Find the range

Problem: x²- 4 / x+2

I did the inverse switching the x and y and got R: (-inf, -2)U(-2, inf)

Please let me know if I did something wrong.

Answer 1

editted

The function has restriction on it's domain at x=-2

since x cannot equal -2, the range also has a discontinuity at y=-4

range would be (-infinity, -4), (-4,+infinity)

unless definition of original function clarified at x=-2, y=-4

as the discontinuity is removable. Then range would be (-infinity,+infinity).

Answer 2