Question

find the domain of (x+2)(1/x+2)

Answer 1

expand 1 + 2x + 2/x + 4 or 5 +2x + 1/x

domain is all real x except x cannot equal zero.

Answer 2

well first, the function is a polynomial. So the initial domain of all polynomials is all real numbers

\[(-\infty, \infty) \]

Now we have to figure out where the function is undefined. We know that if x=-2, then you get:

(0) * (1/0)

And 1/0 is undefined. So the function can never take on the value of x=-2

which means your domain is simply:

\[(-\infty, -2)\cup(-2, \infty)\]