If \(f(x) = 3x^2 - 2x + 1\) and \(g(x) = x - 4\), find \(f(g(2))\).

["# Evaluating Composite Functions: How to Find ( f(g(2)) ) with ( f(x) = 3x^2 - 2x + 1 ) and ( g(x) = x - 4 )", "Understanding composite functions is a key concept in algebra and higher mathematics, especially when analyzing relationships between variables. In this article, we explore how to evaluate ( f(g(2)) ) using two functions:\n[\nf(x) = 3x^2 - 2x + 1 \quad \ ext{and} \quad g(x) = x - 4\n]", "## Step 1: Understand What a Composite Function Is\nA composite function ( f(g(x)) ) means that you first apply the inner function ( g(x) ), then use its output as the input for the outer function ( f(x) ).", "## Step 2: Compute ( g(2) )\nBegin by evaluating the inner function ( g(x) = x - 4 ) at ( x = 2 ):\n[\ng(2) = 2 - 4 = -2\n]", "## Step 3: Substitute ( g(2) ) into ( f(x) )\nNow, substitute the result ( g(2) = -2 ) into ( f(x) ):\n[\nf(g(2)) = f(-2)\n]", "## Step 4: Evaluate ( f(-2) )\nUse the expression for ( f(x) = 3x^2 - 2x + 1 ) with ( x = -2 ):\n[\nf(-2) = 3(-2)^2 - 2(-2) + 1\n]\n[\n= 3(4) + 4 + 1 = 12 + 4 + 1 = 17\n]", "## Final Result\n[\nf(g(2)) = 17\n]", "## Summary\nEvaluating composite functions involves two main steps: first compute the inner function at the given input, then substitute that result into the outer function. In this case:\n- ( g(2) = -2 )\n- ( f(-2) = 3(-2)^2 - 2(-2) + 1 = 17 )", "So, ( f(g(2)) = 17 ). This method is widely used in calculus, physics, and economics to model and simplify complex relationships.", "---", "If you're learning how to evaluate composite functions, practice with different functions and inputs to build confidence in function composition — a foundational skill for advanced math topics.", "---", "Keywords: ( f(x) = 3x^2 - 2x + 1 ), ( g(x) = x - 4 ), composite functions, ( f(g(2)) ), math tutorial, function evaluation, algebra practice."]