Question

Determine discontinuity of the function $y=-\frac{2^{1/x}-1}{2^{1/x}+1}$ at value of is

• A. $x=-1$
• B. $x=0$
• C. $x=1$
• D. $x=2$

Answer 1

The correct option is B $x=0$

$f\left(0^{-}\right)=\underset{h\to 0}{lim}(-\frac{2^{-1/h}-1}{2^{-1/h}+1})=1$
$f\left(0^{-}\right)=\underset{h\to 0}{lim}(-\frac{2^{1/h}-1}{2^{1/h}+1})=-1$
$\Rightarrow LHL\ne RHL\Rightarrow$ Non removable-finite discontinuity.