Let f, g: R → R be two functions defined by f(x)= {x sin (1/x), x ≠ 0; 0, x=0} and g(x)=x f(x) Statement I: f is a continuous function at x=0.…

Let $\displaystyle f, g: \mathrm{R} \rightarrow \mathrm{R}$ be two functions defined by $\displaystyle f(x)=\left\{\begin{array}{ll}x \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.$ and $\displaystyle g(x)=x f(x)$Statement I : $\displaystyle f$ is a continuous function at $\displaystyle x=0$. Statement II : $\displaystyle g$ is a differentiable function at $\displaystyle x=0$.