Question

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

• A. $( - \infty,\infty)$
• B. $( - \infty,3 - \sqrt{3}) \cup (3 + \sqrt{3},\infty)$
• C. $( - \infty,1\rbrack \cup \lbrack 5,\infty)$
• D. $\lbrack 0,\infty)$

Answer 1

Answer: (C)

$( - \infty,1\rbrack \cup \lbrack 5,\infty)$

Answer 2

The function $f(x) = \sqrt{\log(x^{2} - 6x + 6)}$ is defined when

$\log(x^{2} - 6x + 6) \geq 0$

⇒ $x^{2} - 6x + 6 \geq 1$⇒ $(x - 5)(x - 1) \geq 0$

This inequality hold if $x \leq 1$ or $x \geq 5$. Hence, the domain of the function will be $( - \infty,1\rbrack \cup \lbrack 5,\infty)$.