Assertion (A): The domain of the function ^ -1 2 x is (- ,-1 2 ] … - Vidyadip

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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