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The domain of the function $f (x) = \log_{10} [1 - \log_{10} (x^{2} - 5 x + 16)] is$

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(2, 3)

[2, 3]

(2, 3]

[2, 3)

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Correct option is A

f (x) is defined if1−log10⁡x2−5x+16>0 and x2−5x+16>0⇒log10⁡x2−5x+16<1 and x−522+394>0⇒x2−5x+16<101=10 ∵x−522+394>0 for all real x⇒ x2 – 5x + 6 < 0⇒ (x – 3) (x – 2) < 0 ⇒ 2 < x < 3∴Domain of f = (2, 3)

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The domain of the function f(x)=log10⁡1−log10⁡x2−5x+16 is

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The domain of the function $f (x) = \log_{10} [1 - \log_{10} (x^{2} - 5 x + 16)] is$