The function f(x) is defined for all real x. If `f(a+b)=f(ab) AA a " and " b " and " f(-(1)/(2))=-(1)/(2)` then find the value of `f(1005).`

Explanation

To find the value of \( f(1005) \) given the function \( f(x) \) defined for all real \( x \) with the properties \( f(a + b) = f(ab) \) and \( f\left(-\frac{1}{2}\right) = -\frac{1}{2} \), we can follow these steps:

### Step 1: Analyze the Functional Equation
We start with the functional equation:
\[ f(a + b) = f(ab) \]
This means that the function \( f \) takes the same value for \( a + b \) and \( ab \).
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