The largest set on which $f ( x ) = \frac { x } { ( x + 1 ) ^ { 2 } }$ is continuous is
A) $( - \infty , \infty )$
B) $( - \infty , 1 ) \cup ( 1 , \infty )$
C) $( - \infty , - 1 ) \cup ( - 1 , \infty )$
D) $( - \infty , - 1 ) \cup ( 1 , \infty )$
E) $( - \infty , - 1 ) \cup ( - 1,1 ) \cup ( 1 , \infty )$

Question

Quizplus · Accepted Answer

The function $f(x) = \frac{x}{(x+1)^2}$ is continuous everywhere except at $x = -1$, where the denominator becomes zero, causing a division by zero. Therefore, the largest set on which $f(x)$ is continuous is $(-\infty, -1) \cup (-1, \infty)$.

The Largest Set on Which f(x)=x(x+1)2f ( x ) = \frac { x } { ( x + 1 ) ^ { 2 } }f(x)=(x+1)2x​

The Largest Set on Which $f ( x ) = \frac { x } { ( x + 1 ) ^ { 2 } }$