The domain of the function $f ( x ) = \frac { 1 } { \log _ { 2 } x }$ is

A) $[ 0 , \infty )$
B) $( 0 , \infty )$
C) $[ 0,1 ) \cup ( 1 , \infty )$
D) $[ 1 , \infty )$
E) $( 0,1 ) \cup ( 1 , \infty )$

Question

The domain of the function $f ( x ) = \frac { 1 } { \log _ { 2 } x }$ is

A) $[ 0 , \infty )$
B) $( 0 , \infty )$
C) $[ 0,1 ) \cup ( 1 , \infty )$
D) $[ 1 , \infty )$
E) $( 0,1 ) \cup ( 1 , \infty )$

Quizplus · Accepted Answer

The function $f(x) = \frac{1}{\log_2 x}$ is defined for all $x > 0$ except $x = 1$, because $\log_2 x$ is undefined at $x = 0$ and equals $0$ at $x = 1$, making the denominator of $f(x)$ zero. Thus, the domain excludes $0$ and $1$, but includes all other positive numbers.

The Domain of the Function f(x)=1log⁡2xf ( x ) = \frac { 1 } { \log _ { 2 } x }f(x)=log2​x1​

The Domain of the Function $f ( x ) = \frac { 1 } { \log _ { 2 } x }$