If f(x) = {(1/(1 + e^1/x), x ≠ 0)(0, x = 0), then f(x) is A. Continuous as well as differentiable at x = 0

Question

If \(\text{f(x)}= \begin{cases} \frac{1}{1+e^{1/x}} & , x \neq 0\\ 0 & , x = 0 \end{cases},\) then f(x) is

A. Continuous as well as differentiable at x = 0

B. Continuous but not differentiable at x = 0

C. Differentiable but not continuous at x = 0

D. None of these

Answer 1

Correct answer is D.

Given that \(\text{f(x)}= \begin{cases} \frac{1}{1+e^{1/x}} & , x \neq 0\\ 0 & , x = 0 \end{cases}\bigg\}\)

Checking continuity at x = 0,

LHL:

Hence, function is neither continuous nor differentiable at x = 0.