A plant biologist is examining genetic sequences and models a transformation using functions. If \(f(x) = x^2 + 1\) and \(g(x) = 2x - 3\), find \(g(f(3))\).

["Title: Understanding Function Composition: Calculating (g(f(3))) Step by Step", "In the world of plant biology, data modeling often relies on mathematical functions to predict growth patterns, gene expression, or environmental adaptations. One common technique involves composing functions to simulate complex relationships—much like how a plant biologist might model how genetic expressions respond to environmental triggers. This article explores a key concept in function composition using real-world inspired logic: evaluating (g(f(3))), where (f(x) = x^2 + 1) and (g(x) = 2x - 3).", "### What is Function Composition?\nFunction composition occurs when the output of one function becomes the input for another, written as (g(f(x))). This mirrors biological systems where one process (represented by (f)) feeds into a downstream process (modeled by (g)). Understanding such transformations helps scientists predict how genetic pathways or biochemical reactions might cascade through a plant’s system.", "### Breaking Down (f(3))\nWe begin by evaluating the inner function (f(3)). Given:\n[\nf(x) = x^2 + 1\n]\nSubstitute (x = 3):\n[\nf(3) = 3^2 + 1 = 9 + 1 = 10\n]\nHere, (f(3)) represents a transformed state—such as a normalized gene expression level or a scaled phenotypic trait—after applying a quadratic model to an input value (e.g., stress level or time post-mutation).", "### Applying (g) to the Result\nNext, we use the output of (f(3)), which is 10, as the input to (g(x)). Given:\n[\ng(x) = 2x - 3\n]\nSubstitute (x = f(3) = 10):\n[\ng(10) = 2(10) - 3 = 20 - 3 = 17\n]\nThis final value—17—can represent a predicted outcome in a biological model, such as a calibrated growth rate or response metric derived from combined genetic and environmental factors.", "### Final Calculation Summary\nTo recap:\n[\ng(f(3)) = g(10) = 2(10) - 3 = 17\n]\nThus, composing these functions yields:\n[\n\boxed{17}\n]", "### Why This Matters in Plant Biology\nWhile plant biologists rarely announce formulae on social media, such mathematical modeling underpins cutting-edge research—from predicting gene network dynamics to simulating stress responses. Viewing transformations as function compositions fosters clearer thinking about how genetic sequences interact with environmental inputs, much like the elegant derivations seen in (g(f(3)) = 17).", "By mastering function composition, scientists empower themselves to decode complexity—one transformation at a time. Whether analyzing RNA sequencing data or crop resilience metrics, the ability to compute and interpret nested functions strengthens both theoretical understanding and practical innovation.", "So next time you see a plant’s genetic response modeled by (g(f(x))), remember: behind the data lies a structured transformation—and one answer is 17."]