The largest set on which $f ( x ) = \frac { 5 x + 3 } { 5 x ^ { 2 } + 3 }$ is continuous is
A) $( - \infty , \infty )$
B) $\left( - \infty , - \frac { 3 } { 5 } \right) \cup \left( - \frac { 3 } { 5 } , \infty \right)$
C) $\left( - \infty , \frac { 3 } { 5 } \right) \cup \left( \frac { 3 } { 5 } , \infty \right)$
D) $\left( - \infty , - \frac { 3 } { 5 } \right) \cup \left( \frac { 3 } { 5 } , \infty \right)$
E) $\left( - \infty , - \frac { 3 } { 5 } \right) \cup \left( - \frac { 3 } { 5 } , \frac { 3 } { 5 } \right) \cup \left( \frac { 3 } { 5 } , \infty \right)$

Question

Quizplus · Accepted Answer

The function $f(x) = \frac{5x + 3}{5x^2 + 3}$ is continuous everywhere because the denominator $5x^2 + 3$ is never zero for any real x (since $5x^2 + 3 > 0$ for all real x).

The Largest Set on Which f(x)=5x+35x2+3f ( x ) = \frac { 5 x + 3 } { 5 x ^ { 2 } + 3 }f(x)=5x2+35x+3​

The Largest Set on Which $f ( x ) = \frac { 5 x + 3 } { 5 x ^ { 2 } + 3 }$