Book: RD Sharma - Mathematics (Volume 1)
Chapter: 4. Inverse Trigonometric Functions
Subject: Maths - Class 12th
Q. No. 3 of Exercise 4.4
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3
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]⋃[
,∞)
