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(D) rational function is discontinuous where its denominator is zero.Set the denominator to zero: $x^2 - 5|x| + 6 = 0$.Since $x^2 = |x|^2$, we can wri

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$4$

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(D) rational function is discontinuous where its denominator is zero.Set the denominator to zero: $x^2 - 5|x| + 6 = 0$.Since $x^2 = |x|^2$, we can write this as $|x|^2 - 5|x| + 6 = 0$.Let $|x| = t$, then $t^2 - 5t + 6 = 0$.Factoring the quadratic: $(t - 2)(t - 3) = 0$.So, $|x| = 2$ or $|x| = 3$.This gives $x = \pm 2$ or $x = \pm 3$.The points of discontinuity are $x = 2, -2, 3, -3$.There are $4$ such points.

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

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