Find the maximum and minimum values, if any, of the following functions given by
(i) `f (x) = |x + 2 | - 1`
(ii) `g(x) = - | x + 1| +3 `
(iii) `h(x) = sin (2x) + 5`
(iv) `f (x) = | sin 4x + 3|`

Explanation

Let's solve the given functions step by step to find their maximum and minimum values.

### (i) Function: \( f(x) = |x + 2| - 1 \)

1. **Identify the critical point**: The expression inside the absolute value, \( x + 2 \), is zero when \( x = -2 \). This is where the function changes behavior.

2. **Evaluate the function in two cases**:
- **Case 1**: When \( x \geq -2 \):
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