Question

Domain of cos inverse of (x^2-4)

Answer 1

Given : The trigonometric term cos inverse of (x^2-4)

To find: Domain of the given term.

Solution:

• Now we have given the term cos^-1 (x^2-4)

• Let it be y, then:

                   y = cos^-1 (x^2-4)

                   cos y = x^2 - 4

• Now cos y has value in [-1,1]

• So:

                   -1 ≤ x^2 - 4 ≤ 1

                   3 ≤ x^2 ≤ 5

                   √3 ≤ |x| ≤ 5

                   x ∈ [-√5, -√3 ] ∪ [√3, √5]

Answer:

                 So the domain is [-√5, -√3 ] ∪ [√3, √5].