The number of points where the function f (x) = \ cases |2 x ^ 2 -...

Here both the modulus function is continuous in its domain.

At $x = - 1$,

$\lim_{x \to - {1}^{-}}\left|2{x}^{2} - 3x - 7\right| = 2 \text{ and } \lim_{x \to - {1}^{+}}\left[4{x}^{2} - 1\right] = 2$

Hence $f\left(x\right)$ is continuous at $x = - 1$

At $x = 1$.

$\lim_{x \to {1}^{-}}\left[4{x}^{2} - 1\right] = 2 \text{ and } \lim_{x \to {1}^{+}}\left|x + 1\right| + \left|x - 2\right| = 3$

Hence, $f\left(x\right)$ is discontinuous at $x = 1$

For $x \in \left(- 1, 1\right)$ the function $f\left(x\right)$ is discontinuous when \left[4{x}^{2} - 1\right] = 0 / 1 / 2$</p><p>i.e when$x \in \left\{\pm \dfrac{1}{\sqrt{2}}, \pm \dfrac{1}{2}, \pm \dfrac{\sqrt{3}}{2}\right\}