Final answer:
The value of f(-3) for the given function is undefined.
Step-by-step explanation:
The function f(x) is given as a piecewise function:
For x < -3, f(x) = x³ + 18x² + 104x + 192
For -3 ≤ x < 3, f(x) = (3x + 9) / (x³ + 4x² + x - 6)
For x ≥ 3, f(x) = √(x² - 9)
To determine the value of f(-3), we need to consider the second piece of the piecewise function. Substituting x = -3 into the function:
f(-3) = (3(-3) + 9) / ((-3)³ + 4(-3)² + (-3) - 6)
Simplifying further:
f(-3) = 0 / 0
The value of f(-3) is undefined.