Find local minimum value of the function f given by `f(x)=3+|x|,x in R`.

Explanation

To find the local minimum value of the function \( f(x) = 3 + |x| \), we will analyze the function step by step.

### Step 1: Understanding the Absolute Value Function
The absolute value function \( |x| \) is defined as:
- \( |x| = x \) when \( x \geq 0 \)
- \( |x| = -x \) when \( x < 0 \)

### Step 2: Expressing the Function in Piecewise Form
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