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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
Assertion (A): The domain of the function $\sec ^{-1} 2 x$ is \[\left(-\infty,-\frac{1}{2}\right] \cup\left[\frac{1}{2}, \infty\right) .\] Reason $(R): \sec ^{-1}(-2)=-\frac{\pi}{4}$
  • A
    Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
  • B
    Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
  • C
    $A$ is true but $R$ is false.
  • D
    $A$ is false but $R$ is true.
✓

Answer

$\sec ^{-1} x$ is defined if $x \leq-1$ or $x \geq 1$.
Hence, $\sec ^{-1} 2 x$ will be defined if $x \leq-\frac{1}{2}$ or $x \geq \frac{1}{2}$
The range of the function $\sec ^{-1} x$ is $[0, \pi]-\left\{\frac{\pi}{2}\right\}$
Hence, $A$ is true and $R$ is false.

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