Question

The function f(x) is continuous at every number in its domain. State the domain. f(x) = √(x² - 4x - 11).

A) All real numbers
B) x ≥ 2
C) x ≤ -2
D) x ∈ (-[infinity], 2] U [4, [infinity])

Answer 1

The domain of the function f(x) = √(x² - 4x - 11) is x ≤ -3 or x ≥ 7.

Step-by-step explanation:

The domain of the function f(x) = √(x² - 4x - 11) is the set of all real numbers for which the expression inside the square root is non-negative. To find this set, we need to solve the inequality x² - 4x - 11 ≥ 0.

We can factor the quadratic equation as (x - 7)(x + 3) ≥ 0. To determine the sign of the expression, we can consider the sign of each factor. (x - 7) is positive when x > 7 and negative when x < 7. (x + 3) is positive when x > -3 and negative when x < -3.

When both factors have the same sign, the product is positive. Therefore, the domain of f(x) is x ≤ -3 or x ≥ 7.