Let $\;f , g :R \to R\;$be two functions defined by $\;f(x)=\{ \begin{matrix}x sin(\large\frac{1}{x}) \;, x \neq 0 \\ 0\;,x=0 \end{matrix}\;$ , and $\;g(x)=x f(x)\;$ Statement I : f is a continuous function at x=0 . Statement II : g is differential function at x=0 .

Question

(a) both statements I and II are false . (b) both statements I and II are true . (c) statements I is true and statement II is false .(d) statements I is false and statement II is true .