The domain of the function f (x)

$f(x)=\frac{1}{\sqrt{[x]^{2}-3[x]+2}}$

Since [x]2 − 3[x] + 2 = 0

if [x]2 − 2[x] − [x] + 2 = 0

[x] ([x] − 2) −1 ([x] − 2) = 0

i.e [x] = 2 or [x] = 1

f(x) is defined only if [x]2 − 3[x] + 2 > 0

i.e ([x] −2) ([x]−1) > 0

[x] > 2 or [x] < 1

i.e [x] ≥ 3 or [x] ≤ 0

i.e x ∈[3, ∞)  or x∈(−∞, 1)

i.e Domain of f(x) is [3, ∞) ∪ (−∞, 1)

i.e (−∞, 1) ∪ [3, ∞)