Write the domain in interval notation.
-$$f ( x ) = \ln ( \sqrt { x + 5 } - 1 )$$
A) $[ - 5 , \infty )$
B) $( - 4 , \infty )$
C) $[ - 4 , \infty )$
D) $( - 5 , \infty )$

Question

Quizplus · Accepted Answer

For the function $f(x) = \ln(\sqrt{x + 5} - 1)$ to be defined, the argument of the logarithm, $\sqrt{x + 5} - 1$, must be greater than 0. Solving the inequality $\sqrt{x + 5} - 1 > 0$ leads to $\sqrt{x + 5} > 1$, which when squared gives $x + 5 > 1$, resulting in $x > -4$. Therefore, the domain is all real numbers greater than -4, which is represented by the interval $(-4, \infty)$.

Write the Domain in Interval Notation f(x)=ln⁡(x+5−1)f ( x ) = \ln ( \sqrt { x + 5 } - 1 )f(x)=ln(x+5​−1)

Write the Domain in Interval Notation $f ( x ) = \ln ( \sqrt { x + 5 } - 1 )$