The domain of `cos^(-1)(x^2-4)` is (a) [3,5] (b) `[-1,1]` (c)`[-sqrt(5),-sqrt(3)]uu[sqrt(3),sqrt(5)` ] (d) `-sqrt(5),-sqrt(3)]nn[-sqrt(5),sqrt(3)]`

Explanation

To find the domain of the function \( \cos^{-1}(x^2 - 4) \), we need to determine the values of \( x \) for which the expression \( x^2 - 4 \) lies within the range of the inverse cosine function, which is defined for values between -1 and 1, inclusive. Therefore, we need to solve the following inequalities:

1. \( x^2 - 4 \geq -1 \)
2. \( x^2 - 4 \leq 1 \)

### Step 1: Solve the first inequality

Starting with the first inequality:
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