The domain of the function ( x^2 - 6x + 6) is - Vidyadip

MCQ

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

A
$( - \infty ,\;\infty )$
B
$( - \infty ,\;3 - \sqrt 3 ) \cup (3 + \sqrt 3 ,\;\infty )$
✓
$( - \infty ,\;1] \cup [5,\;\infty )$
D
$[0,\;\infty )$

✓

Answer

Correct option: C.

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

c
(c) The function $f(x) = \sqrt {\log ({x^2} - 6x + 6)} $ is defined when $\log ({x^2} - 6x + 6) \ge 0$

==> ${x^2} - 6x + 6 \ge 1$ ==> $(x - 5)(x - 1) \ge 0$

This inequality holds if $x \le 1$ or $x \ge 5$.

Hence, the domain of the function will be $( - \infty ,\,1] \cup [5,\,\infty )$.

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