Question

The number of values of $x$ in the interval $[0,1]$ for which the function $f\left(x\right)=\frac{x+3}{|{\log }_{2}x|-6}$ is not defined are

• A. $2$
• B. $3$
• C. $4$
• D. Function exists everywhere $\forall x\in [0,1]$

Answer 1

The correct option is A $2$

$f\left(x\right)=\frac{x+3}{|{\log }_{2}x|-6}$
For this function to be defined, the denominator cannot equal to zero.
$|{\log }_{2}x|-6\ne 0\Rightarrow |{\log }_{2}x|\ne 6\Rightarrow {\log }_{2}x\ne \pm 6\Rightarrow x\ne 2^6,2^{-6}\Rightarrow x\ne 64,\frac{1}{64}$
We know that, for ${\log }_{2}x$ to be defined
$x>0$
When $x\in [0,1]$
Therefore, in $x\in [0,1]$ the function is not defined at $2$ values that are $x=0,\frac{1}{64}$.