Find the numbers at which f is continuous. At which numbers is f discontinuous?
-$$f ( x ) = \frac { x + 5 } { x ^ { 2 } - 11 x + 24 }$$
A) continuous for all real numbers except $x = - 8 , x = - 3$
B) continuous for all real numbers except $x = 8 , x = 3$
C) continuous for all real numbers except $x = - 5 , x = 8$, and $x = 3$
D) continuous for all real numbers except $x = 5 , x = - 8$, and $x = - 3$

Question

Quizplus · Accepted Answer

The function is continuous everywhere except where the denominator is zero. Factoring the denominator $x^2 - 11x + 24 = (x - 8)(x - 3)$, we find that the function is discontinuous at $x = 8$ and $x = 3$, where the denominator equals zero.

Find the Numbers at Which F Is Continuous f(x)=x+5x2−11x+24f ( x ) = \frac { x + 5 } { x ^ { 2 } - 11 x + 24 }f(x)=x2−11x+24x+5​

Find the Numbers at Which F Is Continuous $f ( x ) = \frac { x + 5 } { x ^ { 2 } - 11 x + 24 }$