The domain of 1[x]2−10[x]+16 is

[x]2−10[x]+16>0 [x]2−8[x]−2[x]+16>0 [x][[x]−8]−2[[x]−8]>0 ([x]−2)([x]−8)>0 [x] 8 x<2(or)x≥9

The domain of 1[x]2−10[x]+16 is

[x]2−10[x]+16>0 [x]2−8[x]−2[x]+16>0 [x][[x]−8]−2[[x]−8]>0 ([x]−2)([x]−8)>0 [x] 8 x<2(or)x≥9

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The domain of $\frac{1}{\sqrt{{[x]}^{2} - 10 [x] + 16}}$ is

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(2, 8)

(- \infty, 2) \cup (8, \infty)

(- \infty, 2) \cup [9, \infty)

(- \infty, 2) \cup (9, \infty)

answer is C.

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Detailed Solution

{[x]}^{2} - 10 [x] + 16 > 0

${[x]}^{2} - 8 [x] - 2 [x] + 16 > 0$

$[x] [[x] - 8] - 2 [[x] - 8] > 0$

$([x] - 2) ([x] - 8) > 0$

$[x] < 2 (or) [x] > 8$

$x < 2 (or) x \geq 9$

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The domain of $\frac{1}{\sqrt{{[x]}^{2} - 10 [x] + 16}}$ is