First slide

Functions (XII)

Question

The domain of the function $f (x) = \frac{1}{\sqrt{{}^{10}{C_{x - 1}} - 3 \times^{10} C_{x}}}$ is

Moderate

A

{9, 10, 11}
B

{9, 10, 12}
C

all natural numbers
D

{9, 10}

Solution

Given function is defined if ${}^{10}{C_{x - 1}} > 3^{10} C_{x}$
or $\frac{1}{11 - x} > \frac{3}{x} or 4 x > 33$
or $x \geq 9$
But 10 ≥ x-1 .and 10≥x so x≤10
$∴ x = 9, 10$

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