Assertion (A): The domain of the function sec^-12x is (-∞, -1/2] ∪ [1/2, ∞)

Question

In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

Assertion (A): The domain of the function sec^-12x is \((-\infty, - \frac12] \cup[\frac 12, \infty)\)

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 1

Correct option is (c) A is true but R is false.

sec^-1x is defined if x ≤ −1 or x ≥ 1. Hence, sec^-12x will be defined if x ≤ −1/2 or x ≥ 1/2.

Hence, A is true.

The range of the function sec^-1x is [0, π] - {π/2}

R is false.