Question: If $ f(x) = 2x + 3 $ and $ g(x) = x^2 - 1 $, compute $ f(g(2)) $.
["Understanding Function Composition: Compute $ f(g(2)) $", "When working with functions in mathematics, computing compositions like $ f(g(x)) $ is a fundamental skill. In this article, we’ll walk through step-by-step how to calculate $ f(g(2)) $, using two specific functions: $ f(x) = 2x + 3 $ and $ g(x) = x^2 - 1 $. This process demonstrates how nested function evaluation works and reinforces key concepts in algebra and function theory.", "---", "### What Does Function Composition Mean?", "The composition $ f(g(x)) $, read as “$ f $ of $ g(x) $”, means you first evaluate the inner function $ g(x) $, then use its result as the input for the outer function $ f $.", "This concept is essential in calculus, computer science, engineering, and more—where complex problems are broken down into simpler function evaluations.", "---", "### Step 1: Evaluate the Inner Function $ g(2) $", "We start with the input $ x = 2 $ and compute $ g(2) $ using the given definition:", "[\ng(x) = x^2 - 1\n]", "Substitute $ x = 2 $:", "[\ng(2) = (2)^2 - 1 = 4 - 1 = 3\n]", "So, $ g(2) = 3 $.", "---", "### Step 2: Use the Result as Input for $ f $", "Now, plug this result into the outer function $ f(x) = 2x + 3 $:", "[\nf(g(2)) = f(3)\n]", "Evaluate $ f(3) $:", "[\nf(3) = 2(3) + 3 = 6 + 3 = 9\n]", "---", "### Final Result", "Putting it all together:", "[\nf(g(2)) = f(3) = 9\n]", "---", "### Summary", "Computing $ f(g(2)) $ involves two key steps:\n1. Evaluate $ g(2) = 3 $\n2. Use that result in $ f(3) = 9 $", "So, $ f(g(2)) = 9 $. Function composition tells us that order matters—always compute the inner function first.", "Mastering such nested function evaluations builds a strong foundation for advanced math and real-world applications involving mathematical modeling, programming, and data transformation.", "---", "Keywords for SEO:\nfunction composition, compute f(g(x)), step-by-step math, evaluate nested functions, how to compute f(g(x)), f(x) = 2x + 3, g(x) = x² - 1, mathematical problem solving, algebra examples", "Meta Description:\nLearn how to compute $ f(g(2)) $ with functions $ f(x) = 2x + 3 $ and $ g(x) = x^2 - 1 $. Step-by-step guide showing substitution and evaluation."]
