Question

Find the domain of definition of `f(x)=cos^-1(x^2-4)`

Answer 1

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]`.