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][,∞)


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