Question

The domain of g(x) = 3/(x + 4) consists of all real numbers except -4​, represented in interval notation as:

A) (-[infinity], -4)
B) (-4, [infinity])
C) (-[infinity], -4] ∪ [-4, [infinity])
D) (-[infinity], [infinity])

Answer 1

The domain of g(x) = 3/(x + 4) is all real numbers except -4, which is when the denominator would be zero. Hence, the correct interval notation is (-∞, -4) ∪ (-4, ∞), which corresponds to option C.

Step-by-step explanation:

The domain of the function g(x) = 3/(x + 4) consists of all real numbers except for the value where the denominator equals zero. In this function, that value is -4. Therefore, the domain excludes -4 to prevent division by zero. The appropriate interval notation that represents this domain is (−∞, -4) ∪ (-4, ∞), which is equivalent to saying 'all real numbers except -4'. Therefore, the correct answer is option C: (−∞, -4] ∪ [-4, ∞).