Find the numbers at which f is continuous. At which numbers is f discontinuous?
-$$f ( x ) = \frac { 3 x - 1 } { x ^ { 2 } - 25 }$$
A) continuous for all real numbers except $x = - 5$ and $x = 5$
B) continuous for all real numbers except $x = - 5 , x = 5$ and $x = - \frac { 1 } { 3 }$
C) continuous for all real numbers except $x = 5$
D) continuous for all real numbers

Question

Quizplus · Accepted Answer

The function $f(x) = \frac{3x - 1}{x^2 - 25}$ is continuous everywhere except where the denominator is zero. The denominator $x^2 - 25$ is zero when $x^2 = 25$, which gives $x = 5$ and $x = -5$. Therefore, the function is discontinuous at $x = 5$ and $x = -5$, and continuous everywhere else.

Find the Numbers at Which F Is Continuous f(x)=3x−1x2−25f ( x ) = \frac { 3 x - 1 } { x ^ { 2 } - 25 }f(x)=x2−253x−1​

Find the Numbers at Which F Is Continuous $f ( x ) = \frac { 3 x - 1 } { x ^ { 2 } - 25 }$