The largest set on which $f ( x ) = \frac { x + 4 } { | x + 4 | }$ is continuous is
A) $( - \infty , \infty )$
B) $( - \infty , - 4 ) \cup ( - 4 , \infty )$
C) $( - \infty , 4 ) \cup ( 4 , \infty )$
D) $( - \infty , - 4 ) \cup ( 4 , \infty )$
E) $( - \infty , - 4 ) \cup ( - 4,4 ) \cup ( 4 , \infty )$

Question

Quizplus · Accepted Answer

The function $f(x) = \frac{x + 4}{|x + 4|}$ is not defined at $x = -4$ because the denominator becomes zero, causing a division by zero issue. Everywhere else, the function is continuous because both the numerator and the absolute value function in the denominator are continuous. Therefore, the largest set on which $f(x)$ is continuous is $(- \infty, -4) \cup (-4, \infty)$.

The Largest Set on Which f(x)=x+4∣x+4∣f ( x ) = \frac { x + 4 } { | x + 4 | }f(x)=∣x+4∣x+4​

The Largest Set on Which $f ( x ) = \frac { x + 4 } { | x + 4 | }$