The number of point / points where the function $f(x) = \dfrac{1}{x^2-5|x|+6}$ is discontinuous is......

The function $f(x) = \dfrac{1}{x^2-5|x|+6}$ is discontinuous at the points where its denominator is zero.

$x^2 - 5|x| + 6 = 0$

Since $x^2 = |x|^2$, the equation can be written as:

$|x|^2 - 5|x| + 6 = 0$

$(|x| - 2)(|x| - 3) = 0$

$|x| = 2 \Rightarrow x = \pm 2$

$|x| = 3 \Rightarrow x = \pm 3$

The points of discontinuity are $x = -3, -2, 2, 3$.

The number of points where the function is discontinuous is $4$.

Answer: $4$