The domain of the function f(x) = 1 [x] ^ 2 - 3[x] - 10 is (where [...

Given:

$f\left(x\right) = \dfrac{1}{\sqrt{{\left[x\right]}^{2} - 3\left[x\right] - 10}}$$</p><p>For$f\left(x\right)$to be defined,</p><p>${\left[x\right]}^{2} - 3\left[x\right] - 10 > 0$</p><p>$⇒ \left(\left[x\right] - 5\right)\left(\left[x\right] + 2\right) > 0$</p><p>$⇒ \left[x\right] 5$</p><p>$⇒ x < - 2 \text{$and$} x \ge 6$</p><p>So, domain is \left(- \infty , - 2\right) \cup [ 6, \infty )$.