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).
✓
(A) is true but (R) is false.
D
(A) is false but (R) is true.

✓

Answer

Correct option: C.

(A) is true but (R) is false.

(c) : $\sec ^{-1} x$ 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, Assertion is true and Reason is false.

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