Question

Find the domain of `sec^(-1)(3x-1)`.

Answer 1

The range of sec x is the domain of sec⁻¹ x

Now,

The range of sec x is (−∞, −1] ∪ [1, ∞)

∴ The domain of a given function would be

3x − 1 ≤ −1 and 3x − 1 ≥ 1

3x ≤ 0 and 3x ≥ 2

x ≤ 0 and x ≥ `2/3`

∴ The domain of the given function is (−∞, 0] ∪ [`2/3`, ∞)