Solution: First compute $ g(3) = 3^2 - 4 = 5 $. Then $ f(g(3)) = f(5) = 2(5) + 1 = 11 $. Final answer: $ oxed{11} $.

["# Step-by-Step Solution to Evaluate $ f(g(3)) $ with Clear Mathematical Computation", "Understanding how functions compose is fundamental in algebra and higher mathematics. This article walks you through a clear, step-by-step solution to compute $ f(g(3)) $, demonstrating substitution and function evaluation techniques that form the backbone of complex problem-solving.", "---", "## Step 1: Compute $ g(3) $", "To evaluate a composite function like $ f(g(3)) $, we start from the inner function and compute $ g(3) $ first. According to the problem definition:", "$$\ng(3) = 3^2 - 4\n$$", "Calculate each term:", "- $ 3^2 = 9 $\n- Then subtract 4: $ 9 - 4 = 5 $", "So,", "$$\ng(3) = 5\n$$", "---", "## Step 2: Substitute and Compute $ f(g(3)) = f(5) $", "Now that we know $ g(3) = 5 $, we substitute this value into the outer function $ f $:", "$$\nf(g(3)) = f(5)\n$$", "Using the given expression for $ f $:", "$$\nf(5) = 2(5) + 1\n$$", "Perform the multiplication first:", "- $ 2 \ imes 5 = 10 $", "Then add:", "- $ 10 + 1 = 11 $", "Thus,", "$$\nf(5) = 11\n$$", "---", "## Final Answer", "Putting it all together:", "$$\nf(g(3)) = f(5) = \boxed{11}\n$$", "---", "## Why This Matters", "Composing functions $ f(g(x)) $ lets us build complex relationships from simpler ones. Mastering step-by-step substitution ensures accuracy in both theoretical math and real-world applications, such as modeling systems in engineering, economics, and computer science.", "This straightforward example reinforces core algebraic skills—swiftly evaluating expressions and understanding function behavior—essential for advanced study and problem-solving.", "$$\n\bboxed{11}\n$$"]