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 function $\sqrt{\ln(x + 2)}$ consists of two parts: the logarithm $\ln(x + 2)$ and the square root $\sqrt{\cdot}$. For the logarithm to be defined, its argument $x + 2$ must be greater than 0, so $x + 2 > 0$ which simplifies to $x > -2$. For the square root to be defined, the value inside it, which is $\ln(x + 2)$, must be greater than or equal to 0. However, the condition $x > -2$ already ensures that $\ln(x + 2)$ will be defined and can take on positive values as $x$ increases. Therefore, the domain of the function is all $x$ such that $x > -2$, which is $[ - 1 , \infty )$.

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 $f ( x ) = \sqrt { \ln ( x + 2 ) }$