JEE Main 2022 · 28 Jul · Shift 1 · Mathematics Q2

← JEE Main 2022 · 28 Jul · Shift 1

MathematicsSingle correct+4 / -1Question 2 of 90

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

\left(-\infty,\dfrac14\right]

\left[-\dfrac14,\infty\right)

\left(-\dfrac13,\infty\right)

\left(-\infty,\dfrac13\right]

Answer and worked solution

Official answer: B

Condition $-1\le\frac{x^2-4x+2}{x^2+3}\le1$ .

Upper bound gives $-4x+2\le3$ , so $x\ge-\frac14$ . Lower bound gives $2x^2-4x+5\ge0$ , true always.

Domain $\left[-\frac14,\infty\right)$ . (B)

Topics:Inverse trigonometric functions Domain and range

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JEE Main 2022 · 28 Jul · Shift 1, Mathematics question 2