Question

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

Answer 1

Domain of sec-1x is (-∞, -1] ⋃ [1, ∞)

Domain of tan-1x is R

Union of (1) and (2) will be domain of given function

(–∞,–1]⋃[1,∞) ⋃ R ⇒ (–∞,–1]⋃[1,∞)

∴ The domain of given function is (–∞,–1]⋃[1,∞).