Find the domain of definition of f(x) = cos–1(x2–4). – InterviewSolution

1.

Find the domain of definition of f(x) = cos–1(x2–4).

Answer»

Domain of cos^-1x lies in the interval [-1, 1].

Therefore, the domain of cos^–1(x² – 4) lies in the interval [–1, 1].

-1 ≤ x² - 4 ≤ 1

3 ≤ x²≤ 5

±√3 ≤ x ≤ ± √5

-√5 ≤ x ≤ - √3 and √3 ≤ x ≤ √5

Domain of cos^-1(x² - 4) is [-√5, -√3] ⋃ [√3, √5].

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