The domain of the function ⁻¹ (x^2-4 ) is

Step-by-step solution

The domain of the function f(x) = ⁻¹(u) is defined by the condition -1 u 1 . For the given function f(x) = ⁻¹(x^2 - 4) , we must have -1 x^2 - 4 1 . Adding 4 to all parts of the inequality: 3 x^2 5 . This inequality implies two conditions: x^2 3 and x^2 5 . Solving x^2 3 gives x (- , - 3 ] [ 3 , ) . Solving x^2 5 gives x [- 5 , 5 ] . The domain is the intersection of these two sets: ([- , - 3 ] [ 3 , ]) [- 5 , 5 ] = [- 5 , - 3 ] [ 3 , 5 ] . Answer: [- 5 ,- 3 ] [ 3 , 5 ]