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प्रश्न
Find the domain of `sec^(-1)(3x-1)`.
उत्तर
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`, ∞)
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