Step 1 :Consider the following functions: \(f(x)=|x|\) and \(g(x)=x-2\).
Step 2 :To find \((f \cdot g)(1)\), we need to evaluate the functions \(f(x)\) and \(g(x)\) at \(x=1\) and then multiply the results.
Step 3 :The function \(f(x)\) is the absolute value of \(x\) and the function \(g(x)\) is \(x-2\). So, we need to find \(f(1)\) and \(g(1)\) and then multiply these values.
Step 4 :Final Answer: The value of \((f \cdot g)(1)\) is \(\boxed{-1}\).