The domain of f(x)=log(x2-6x+6) is

Given,f(x)=log (x2-6x+6 ⇒log (x2-6x+6)≥0 and x2-6x+6>0 ⇒x2-6x+6≥1 ⇒x2-6x+5≥0 ⇒(x-5)(x-1)≥0 ∴x∈(-∞,1]∪[5,∞)

The domain of f(x)=log(x2-6x+6) is

Given,f(x)=log (x2-6x+6 ⇒log (x2-6x+6)≥0 and x2-6x+6>0 ⇒x2-6x+6≥1 ⇒x2-6x+5≥0 ⇒(x-5)(x-1)≥0 ∴x∈(-∞,1]∪[5,∞)

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The domain of f(x)= $\sqrt{\log (x^{2} - 6 x + 6)}$ is

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(- $\infty, \infty)$

[3- $\sqrt{3}$ ,3+ $\sqrt{3}$ ]

( $- \infty, 1] \cup [5, \infty)$

[0, $\infty$ )

answer is C.

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Detailed Solution

Given,f(x)=

$\sqrt{\log (x^{2} - 6 x + 6} \Rightarrow \log (x^{2} - 6 x + 6) \geq 0 a n d x^{2} - 6 x + 6 > 0 \Rightarrow x^{2} - 6 x + 6 \geq 1 \Rightarrow x^{2} - 6 x + 5 \geq 0 \Rightarrow (x - 5) (x - 1) \geq 0 ∴ x \in (- \infty, 1] \cup [5, \infty)$

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The domain of f(x)= $\sqrt{\log (x^{2} - 6 x + 6)}$ is