Question:** A middle school student is exploring functions and their compositions. If \(f(x) = 3x - 2\) and \(g(x) = x^2 + 1\), what is \(g(f(4))\)?
["Title: How to Compose Functions: Calculating (g(f(4))) Step-by-Step", "When middle school students first encounter functions and function composition, it can feel tricky—but with a clear step-by-step approach, it becomes an exciting part of algebra! In this article, we’ll walk through a classic function composition problem: what is (g(f(4)))—given (f(x) = 3x - 2) and (g(x) = x^2 + 1)?", "---", "### Understanding Function Composition", "Function composition means plugging the result of one function into another. If you want to compute (g(f(4))), you first evaluate (f(4)), then use that result as the input for (g). Think of it like a pipeline: first (f(4)) processes the input, then (g(f(4))) takes that output and finishes the job.", "---", "### Step 1: Evaluate (f(4))", "Given:\n[\nf(x) = 3x - 2\n]", "Substitute (x = 4):\n[\nf(4) = 3(4) - 2 = 12 - 2 = 10\n]", "---", "### Step 2: Evaluate (g(f(4)) = g(10))", "Now that we know (f(4) = 10), we plug this into (g(x)):\nGiven:\n[\ng(x) = x^2 + 1\n]", "Substitute (x = 10):\n[\ng(10) = 10^2 + 1 = 100 + 1 = 101\n]", "---", "### Final Result", "Putting it all together:\n[\ng(f(4)) = g(10) = 101\n]", "So, the value of (g(f(4))) with (f(x) = 3x - 2) and (g(x) = x^2 + 1) is 101.", "---", "### Why This Matters in Middle School Math", "Working with function composition builds critical thinking and problem-solving skills. It helps students understand how multiple relationships work together, a concept used in everything from science modeling to computer programming.", "By mastering simple function compositions like (g(f(4))), you’re laying a strong foundation for more complex topics like inverse functions and real-world applications in engineering and economics.", "---", "### Summary:\n- Compose functions by evaluating the inner function first.\n- (f(4) = 10)\n- (g(10) = 101)\n- Therefore, (g(f(4)) = 101)", "Keep practicing function composition with different functions—you’ll soon solve these problems confidently and recognize their power in math and beyond!", "---", "Tags: function composition middle school, (g(f(x))) explained, middle school algebra, (f(x) = 3x - 2), (g(x) = x^2 + 1), how to compute (g(f(4)))", "Meta Description:\nDiscover how to compute (g(f(4))) using the functions (f(x) = 3x - 2) and (g(x) = x^2 + 1). Step-by-step solution for middle school students mastering function composition."]
