Find the maximum and minimum values, if any, of the following functionsgiven 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) \( f(x) = |x + 2| - 1 \)

1. **Identify the critical points**: The expression inside the absolute value, \( x + 2 \), is zero when \( x = -2 \). This is a critical point.
2. **Evaluate \( f(x) \) at the critical point**:
\[
f(-2) = |-2 + 2| - 1 = |0| - 1 = -1
...