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

For the function $f(x) = \sqrt{\ln(x - 5)}$ to be defined, two conditions must be met: 1) $x - 5 > 0$, ensuring the argument of the logarithm is positive, and 2) the value inside the square root must be non-negative, which is inherently satisfied by the nature of the logarithm function for positive arguments. Solving $x - 5 > 0$ gives $x > 5$. However, since the square root also requires its argument to be non-negative, and the logarithm of values greater than 1 is non-negative, the smallest value inside the logarithm that satisfies this is when $x - 5 = 1$, or $x = 6$, making the domain $[6, \infty)$.

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 $f ( x ) = \sqrt { \ln ( x - 5 ) }$