Find the domain of

sec^–1 (3x–1)

The range of sec x is the domain of sec^–1x

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 ≥

∴ The domain of the given function is (–∞,0]⋃[,∞)