1.
Let R\mathbb{R} denote the set of all real numbers. Define the function f:R→Rf: \mathbb{R} \to \mathbb{R} by
f(x)={2−2x2−x2sin⁡1xif x≠0,2if x=0.f(x) = \begin{cases} 2 - 2x^2 - x^2 \sin \frac{1}{x} & \text{if } x \neq 0, \\ 2 & \text{if } x = 0. \end{cases}

Then which one of the following statements is TRUE?