QJEEM22Ma2fa6: JEE Main 2022 Mathematics - Class 12 JEEM22Ma2fa6 Solution: The domain of the function f ( x ) = cos − 1 ( x 2 − 5 x + 6 x…

Question

Verified Solution • 2025–26 Session moderate

The domain of the function

$f (x) = \frac{\cos^{- 1} (\frac{x^{2} - 5 x + 6}{x^{2} - 9})}{\log_{e} (x^{2} - 3 x + 2)}$ is :

Accepted Answer

-1 \leq \frac{x^{2}-5 x+6}{x^{2}-9} \leq 1

and

x^{2}-3 x+2&gt;0, \neq 1

\frac{(x - 3) (2 x + 1)}{x^{2} - 9} \geq 0 ∣ \frac{5 (x - 3)}{x^{2} - 9} \geq 0

The solution to this inequality is

x \in\left[\frac{-1}{2}, \infty\right)-\{3\}

for

x^{2}-3 x+2&gt;0

and

\neq 1

x \in (- \infty, 1) \cup (2, \infty) - {\frac{3 - \sqrt{5}}{2}, \frac{3 + \sqrt{5}}{2}}

Combining the two solution sets (taking intersection)

x \in [- \frac{1}{2}, 1) \cup (2, \infty) - {\frac{3 - \sqrt{5}}{2}, \frac{3 + \sqrt{5}}{2}}

Step-by-Step Verified Solution