The domain of the function f(x)=1 10Cx−1−3×10Cx contains the points

Given function is defined if 10Cx−1>310Cxor 111−x>3x or 4x>33 or x≥9 But x≤10∴ x=9,10

The domain of the function f(x)=1 10Cx−1−3×10Cx contains the points

Given function is defined if 10Cx−1>310Cxor 111−x>3x or 4x>33 or x≥9 But x≤10∴ x=9,10

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

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9,10, 11

9,10,12

all natural numbers

9,10

answer is D.

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Detailed Solution

Given function is defined if $^{10} C_{x - 1} > 3^{10} C_{x}$
or $\frac{1}{11 - x} > \frac{3}{x} or 4 x > 33$
$\begin{array}{ll} or x \geq 9 \\ But x \leq 10 \\ ∴ x = 9, 10 \end{array}$

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