# Domain of the function $f(x) = \frac{1}{\sqrt{10_{C_{x-1}}-3 . 10_{C_x}}}$ contains the points

Q: Domain of the function $\Large f(x) = \frac{1}{\sqrt{10_{C_{x-1}}-3 . 10_{C_x}}}$ contains the points

(A) 9, 10, 11

(B) 9, 10, 12

(C) all natural numbers

(D) none of these

Sol. Given function is defined if $\large 10_{C_{x-1}} > 3. 10_{C_x}$

$\large \frac{1}{11-x} > \frac{3}{x}$

⇒ 4x > 33

⇒ x  ≥  9 but x ≤ 10

⇒ x = 9, 10

Hence (D) is the correct answer.