Write the domain in interval notation.
-$$f ( x ) = \log \left( \frac { 1 } { \sqrt { x + 15 } } \right)$$
A) $( - \infty , - 15 ]$
B) $[ - 15 , \infty )$
C) $( - \infty , - 15 )$
D) $( - 15 , \infty )$

Question

Quizplus · Accepted Answer

The domain of a logarithmic function is all the values of $x$ for which the argument of the logarithm is positive. Since the argument here is $\frac{1}{\sqrt{x+15}}$, we need $x+15 > 0$ for the square root to be defined and positive. Solving $x+15 > 0$ gives $x > -15$, which corresponds to the interval $(-15, \infty)$.

Write the Domain in Interval Notation f(x)=log⁡(1x+15)f ( x ) = \log \left( \frac { 1 } { \sqrt { x + 15 } } \right)f(x)=log(x+15​1​)

Write the Domain in Interval Notation $f ( x ) = \log \left( \frac { 1 } { \sqrt { x + 15 } } \right)$