Find the domain of the function.
-$$f ( x ) = \log _ { 10 } \left( x ^ { 2 } - 16 x + 63 \right)$$
A) $( 9 , \infty )$
B) $( - \infty , 7 ) \cup ( 9 , \infty )$
C) $( - 7,9 )$
D) $( - \infty , - 7 )$

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 the given function, we need $x^2 - 16x + 63 > 0$. Factoring the quadratic expression, we get $(x - 7)(x - 9) > 0$. Solving this inequality, we find that the solution is $x < 7$ or $x > 9$, which corresponds to the union of two intervals: $(- \infty , 7 ) \cup ( 9 , \infty )$.

Find the Domain of the Function f(x)=log⁡10(x2−16x+63)f ( x ) = \log _ { 10 } \left( x ^ { 2 } - 16 x + 63 \right)f(x)=log10​(x2−16x+63)

Find the Domain of the Function $f ( x ) = \log _ { 10 } \left( x ^ { 2 } - 16 x + 63 \right)$