Find the domain of the function.
-$f ( x ) = \log _ { 10 } \left( x ^ { 2 } - 11 x + 18 \right)$
A) $( - \infty , 2 ) \cup ( 9 , \infty )$
B) $( 9 , \infty )$
C) $( - 2,9 )$
D) $( - \infty , - 2 )$

Question

Quizplus · Accepted Answer

The domain of a logarithmic function is all the x-values for which the argument of the logarithm is greater than zero. For $f(x) = \log_{10}(x^2 - 11x + 18)$, we need $x^2 - 11x + 18 > 0$. Factoring the quadratic gives $(x - 2)(x - 9) > 0$, which is true for $x < 2$ or $x > 9$. Therefore, the domain is $(-\infty, 2) \cup (9, \infty)$.

Find the Domain of the Function f(x)=log⁡10(x2−11x+18)f ( x ) = \log _ { 10 } \left( x ^ { 2 } - 11 x + 18 \right)f(x)=log10​(x2−11x+18)

Find the Domain of the Function $f ( x ) = \log _ { 10 } \left( x ^ { 2 } - 11 x + 18 \right)$