First slide

Functions (XII)

Question

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

Moderate

A

(- $\infty, \infty)$
B

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

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

[0, $\infty$ )

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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