Let f, g: R → R be two functions defined by


Let $f, g: R \rightarrow R$ be two functions defined byf $(x)=$ $\left\{\begin{array}{l}x \sin \left(\frac{1}{x}\right), x \neq 0 \\ 0 \quad, x=0\end{array}\right.$, and $g(x)=x f(x):-$

Statement I : $\mathrm{f}$ is a continuous function at $\mathrm{x}=0$.

Statement II : $\mathrm{g}$ is a differentiable function at $\mathrm{x}=0$.

  1. Statement I is false and statement II is true

  2. Statement I is true and statement II is false

  3. Both statement I and II are true

  4. Both statements I and II are false

Correct Option: 3,


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