Given $f(0) = 0$ and $f(x) = \frac{1}{(1 - e^{- 1/x})}$ for$x
eq 0$. Then only one of the follo0wing statements on $f(x)$ is true. That id $f(x)$, is

Question

Given $f(0) = 0$ and $f(x) = \frac{1}{(1 - e^{- 1/x})}$ for$x 
eq 0$. Then only one of the follo0wing statements on $f(x)$ is true. That id $f(x)$, is

Dr. Abubacker · Accepted Answer

(b)
At $x = 0$,
LHL$= \lim_{h ightarrow 0}{\frac{1}{1 - e^{- 1/(0 - h)}} = \lim_{h ightarrow 0}{\frac{1}{1 - e^{1/h}} =}0}$
RHL$= \lim_{h ightarrow 0}{\frac{1}{1 - e^{- 1/(0 + h)}} = \lim_{h ightarrow 0}{\frac{1}{1 - e^{- 1/h}} =}1}$
$	herefore$ FUnction is not continuous at $x = 0$

Q. Given $f(0) = 0$ and $f(x) = \frac{1}{(1 - e^{- 1/x})}$ for$x \neq 0$. Then only one of the follo0wing statements on $f(x)$ is true. That id $f(x)$, is

Explanation

Reviewed by Dr. Abubacker

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