Answer:
(-∞, -5) U (-5, -1) U (-1, +∞)
Explanation:
To determine the domain of the function k(x) = (x - 6)/(x^2 + 6x + 5), we need to identify any values of x that would result in division by zero.
First, let's factor the denominator: x^2 + 6x + 5 = (x + 1)(x + 5).
To avoid division by zero, we need to exclude any values of x that would make the denominator equal to zero. In this case, x cannot be -1 or -5.
Therefore, the domain of the function k(x) is all real numbers except x = -1 and x = -5.
In interval notation, we can express the domain as:
(-∞, -5) U (-5, -1) U (-1, +∞)