Find the domain of the function.
-$$f ( x ) = \log _ { 5 } \left( 25 - x ^ { 2 } \right)$$
A) $( \infty , - 5 ) \cup ( 5 , \infty )$
B) $( - 5,5 )$
C) $[ - 5,5 ]$
D) $( - 25,25 )$

Question

Quizplus · Accepted Answer

The argument of the logarithm, $25 - x^2$, must be greater than 0 for the function to be defined. Solving $25 - x^2 > 0$ gives $x^2 < 25$, which implies $-5 < x < 5$. Therefore, the domain is $(-5, 5)$.

Find the Domain of the Function f(x)=log⁡5(25−x2)f ( x ) = \log _ { 5 } \left( 25 - x ^ { 2 } \right)f(x)=log5​(25−x2)

Find the Domain of the Function $f ( x ) = \log _ { 5 } \left( 25 - x ^ { 2 } \right)$