True/False Question :
There exists a function $f:\mathbb{R} \rightarrow \mathbb{R}$ satisfying,
$f\left ( -1 \right )=-1, f(1)=1$ and $\left | f\left ( x \right )-f\left ( y \right )\left | \leq \right |x-y \right |^{\frac{3}{2}},$ for all $x,y \in \mathbb{R}.$