Question

The domain of both f(x) = x - 6 and g(x) = x + 6 is all real numbers. What is the domain of h(x) = f(x)/g(x)?

Answer 1

This is a quotient (division) of two functions we must be concerned with the fact that division by zero is undefined.

Since g(x) is in the divisor position, it cannot equal 0.
$x+6 \neq 0$
$x \neq -6$ Subtract 6 from both sides to solve.
So the domain is all real numbers except -6
Set notation {x | x ∈ R, x ≠ -6}
Interval notation (-∞,-6)∪(-6,∞)