Question

The domain of the function \[ f(x) = \frac{1}{\log(1 - x)} + \sqrt{x + 2} \] is

• A. \( [-3, -2] \cup [0, \infty) \)
• B. \( [-3, 2] \)
• C. \( [0, \infty) \)
• D. \( [-3, -2] \cup [2, \infty) \)

Hint:

To find the domain of a function, check the constraints on logarithms and square roots to ensure the arguments are within the allowed range.

Answer 1

The Correct Option is B

Step 1: Determining the domain.
The domain of the function is determined by the constraints on the logarithmic and square root terms. The function is valid when \( 1 - x>0 \) and \( x + 2 \geq 0 \). Solving these inequalities gives \( [-3, 2] \).

Step 2: Conclusion.
The domain of the function is \( [-3, 2] \), corresponding to option (2).