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Question
Find the domain of definition of `f(x)=cos^-1(x^2-4)`
Solution
For `cos^-1 (x^2 - 4)` to be defined
`-1 ≤ x^2 - 4 ≤ 1`
⇒ `3 ≤ x^2 ≤ 5`
⇒ `x in [- sqrt5, - sqrt3 ] cup [sqrt3, sqrt5 ] `
Hence, the domain of `f(x) is [-sqrt5, -sqrt3] cup [sqrt3, sqrt5]`.
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