The domain of the function f(x) = 1/(x² + 3x + 2) is (-∞, -2) ∪ (-2, -1) ∪ (-1, ∞).
The domain of the function f(x) = 1/(x² + 3x + 2) is all real numbers except for the values of x that cause the denominator to equal zero. In this case, the denominator is:
x² + 3x + 2 = 0
We can find the values of x that make the denominator zero by solving the quadratic equation x² + 3x + 2 = 0. Using the quadratic formula, we get:
x = (-3 ± √(3² - 412)) / (2*1)
x = (-3 ± √(9 - 8)) / 2
x = (-3 ± √1) / 2
x = (-3 + 1) / 2 or x = (-3 - 1) / 2
x = -2 / 2 or x = -4 / 2
x = -1 or x = -2
Therefore, the domain of the function f(x) = 1/(x² + 3x + 2) is all real numbers except x = -1 and x = -2. In interval notation, the domain is: (-∞, -2) ∪ (-2, -1) ∪ (-1, ∞)
Complete question:
The domain of the function f(x) = 1/(x² + 3x + 2) is