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)" "=" "s in" "(2x)" "+" "5`

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. **Understanding the Absolute Value**:
The expression \( |x + 2| \) is always non-negative. It equals zero when \( x + 2 = 0 \) or \( x = -2 \). Therefore, \( |x + 2| \geq 0 \).

2. **Finding the Range of \( f(x) \)**:
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