MHT CET · Maths · Functions
The domain of the function \(\log _{10}\left(x^2-5 x+6\right)\) is
- A \((-\infty, \infty)\)
- B \((-\infty, 2) \cup(3, \infty)\)
- C \((2,3)\)
- D None of these
Answer & Solution
Correct Answer
(B) \((-\infty, 2) \cup(3, \infty)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{f}(\mathrm{x})=\log _{10}\left(\mathrm{x}^2-5 \mathrm{x}+6\right) \\ & \therefore \mathrm{x}^2-5 \mathrm{x}+6>0 \Rightarrow(\mathrm{x}-2)(\mathrm{x}-3)>0 \\ & \Rightarrow \mathrm{x}>3 \text { or } \mathrm{x} < 2 \\ & \therefore \mathrm{x} \in(-\infty, 2) \cup(3, \infty)\end{aligned}\)
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