Q69 / 150 · MHT CET 2021 (24 Sep Shift 1) · Mathematics

The domain of the function $\log _{10}\left(x^2-5 x+6\right)$ is

  • A
    $(-\infty, \infty)$
  • Correct answer
    B
    $(-\infty, 2) \cup(3, \infty)$
  • C
    $(2,3)$
  • D
    None of these

Solution

$\begin{aligned} & \mathrm{f}(\mathrm{x})=\log _{10}\left(\mathrm{x}^2-5 \mathrm{x}+6\right) \\ & \therefore \mathrm{x}^2-5 \mathrm{x}+6>0 \Rightarrow(\mathrm{x}-2)(\mathrm{x}-3)>0 \\ & \Rightarrow \mathrm{x}>3 \text { or } \mathrm{x} < 2 \\ & \therefore \mathrm{x} \in(-\infty, 2) \cup(3, \infty)\end{aligned}$

Hence, the correct answer is option: 'B'.

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