Q106 / 180 · KCET 2025 · Mathematics

A function is $f(x)=\left\{\begin{array}{cc}\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}, & \text { if } x \neq 0 \\ 0, & \text { if } x=0\end{array}\right.$

  • A
    continuous at $\mathrm{x}=0$
  • Correct answer
    B
    not continuous at $\mathrm{x}=0$
  • C
    differentiable at $\mathrm{x}=0$
  • D
    differentiable at $\mathrm{x}=0$, but not continuous at $\mathrm{x}=0$

Solution

$f(x)=\left\{\begin{array}{cc} \frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1} & , \quad x \neq 0 \\ 0 & , x=0 \end{array}\right.$ LHL $=-1$, RHL $=1$, Not continuous.

Hence, the correct answer is option: 'B'.

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