The largest set on which $f ( x ) = \sqrt { x ^ { 2 } + 1 }$ 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

The largest set on which $f ( x ) = \sqrt { x ^ { 2 } + 1 }$ 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) $( - \infty , - 1 ) \cup ( - 1,1 ) \cup ( 1 , \infty )$

Quizplus · Accepted Answer

The function $f(x) = \sqrt{x^2 + 1}$ is continuous for all real numbers because the inside of the square root, $x^2 + 1$, is always positive, and the square root function is continuous wherever its argument is non-negative.

The Largest Set on Which f(x)=x2+1f ( x ) = \sqrt { x ^ { 2 } + 1 }f(x)=x2+1​

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