Find the domain of the function below.
$f ( x ) = \sqrt { \ln ( x - 5 ) }$
A) $( - \infty , 5 ]$
B) $( - \infty , 6 ]$
C) $[ 5 , \infty )$
D) $[ 6 , \infty )$
E) $( 0 , \infty )$

Question

Quizplus · Accepted Answer

The domain of a square root function requires that the radicand (expression inside the square root) be greater than or equal to zero.
Thus, we must have $\ln(x-5) \geq 0$.

Solving for x, we have:
$$\ln(x-5) \geq 0$$
$$e^{\ln(x-5)} \geq e^0$$
$$x-5 \geq 1$$
$$x \geq 6$$

Therefore, the domain of the function is $[6, \infty)$.

Find the Domain of the Function Below f(x)=ln⁡(x−5)f ( x ) = \sqrt { \ln ( x - 5 ) }f(x)=ln(x−5)​

Find the Domain of the Function Below $f ( x ) = \sqrt { \ln ( x - 5 ) }$