Verified Solution • 2025–26 Session moderate

QJEEM22Ma0c92: JEE Main 2022 Mathematics - Class 12 JEEM22Ma0c92 Solution: Considering only the principal values of the inverse…

Considering only the principal values of the inverse trigonometric functions, the domain of the function f(x)=cos⁡−1(x2−4x+2x2+3)f(x)=\cos ^{-1}\left(\frac{x^{2}-4 x+2}{x^{2}+3}\right) is :

Multiple Choice Options

  • A (−∞,14]\left(-\infty, \frac{1}{4}\right]
  • B [−14,∞)\left[-\frac{1}{4}, \infty\right)
  • C (−1/3,∞)(-1 / 3, \infty)
  • D (−∞,13]\left(-\infty, \frac{1}{3}\right]

Step-by-Step Verified Solution

−1≤x2−4x+2x2+3≤1- 1 \le {{{x^2} - 4x + 2} \over {{x^2} + 3}} \le 1

⇒−x2−3≤x2−4x+2≤x2+3\Rightarrow - {x^2} - 3 \le {x^2} - 4x + 2 \le {x^2} + 3

⇒2x2−4x+5≥0\Rightarrow 2{x^2} - 4x + 5 \ge 0 & −4x≤1- 4x \le 1

x∈Rx \in R & x≥−14x \ge - {1 \over 4}

So domain is [−14,∞)\left[ { - {1 \over 4},\infty } \right)

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