Find the domain of the function below.
$f ( x ) = \sqrt { \ln ( x + 2 ) }$
A) $( - \infty , - 2 ]$
B) $( - \infty , - 1 ]$
C) $[ - 2 , \infty )$
D) $[ - 1 , \infty )$
E) $( 0 , \infty )$

Question

Quizplus · Accepted Answer

The domain of the function is the set of values of x for which the function is defined. In this case, the function is defined only when the argument of the logarithm is positive or zero and the argument of the square root is nonnegative. Therefore, we must solve the following inequality for x:
$$\ln(x+2)\geq0$$
This inequality is satisfied for x greater than or equal to -1, so the domain of the function is:
$$[-2,\infty)$$ 
Note that since the domain includes -2 but excludes -1, choices A and B are incorrect. Furthermore, since the domain includes nonnegative values, choice E is also incorrect. Thus, the only correct choice is D.

Find the Domain of the Function Below f(x)=ln⁡(x+2)f ( x ) = \sqrt { \ln ( x + 2 ) }f(x)=ln(x+2)​

Find the Domain of the Function Below $f ( x ) = \sqrt { \ln ( x + 2 ) }$