If domain of f(x) is (– ∞, 0], then domain of $f(6\{x\}^2- 5\{x\} +1)$ is (where {·} represents fractional part function

$\underset{n∈I}{U}\left[n+\frac{1}{3},n+\frac{1}{2}\right]$ (– ∞, 0) $\underset{n∈I}{U}\left[n+\frac{1}{6},n+1\right]$ none of these

$\underset{n∈I}{U}\left[n+\frac{1}{3},n+\frac{1}{2}\right]$

∵ domain of f (x) is (– ∞, 0] $∴ 6\{x\}^2- 5\{x\} +1≤0$ $⇒(2\{x\}-1)(3\{x\}-1)≤0⇒\frac{1}{3}≤\{x\}≤\frac{1}{2}⇒x∈\underset{n∈I}{U}\left[n+\frac{1}{3},n+\frac{1}{2}\right]$