Let $f(x)=\frac{1}{[x]}+\sqrt{(2-x)x}$ and [.] denotes the greatest integer, then the domain of f is
Answer & explanation
Correct answer: option 3
For $D_f, f(x)$ must be real
$⇒ [x] ≠ 0$ and $(2 − x)x ≥ 0⇒ x ∉ [0, 1)$ and
$0 ≤ x ≤ 2 ⇒ x ∈ [1, 2] ⇒ D_f = [1, 2]$