To find \( G(3) \), substitute \( t = 3 \) into the function \( G(t) = rac{4t^2 + 3}{t - 1} \).
["# How to Find ( G(3) ): Substitute ( t = 3 ) into the Function ( G(t) = \frac{4t^2 + 3}{t - 1} )", "Understanding how to evaluate a function at a specific value is a fundamental skill in algebra and calculus. Whether you're working on academic problems, data modeling, or real-world applications, knowing how to substitute values into functions ensures accurate results. In this article, we’ll walk through the step-by-step process of finding ( G(3) ) for the function:", "[\nG(t) = \frac{4t^2 + 3}{t - 1}\n]", "## What Does It Mean to Find ( G(3) )?", "Finding ( G(3) ) means calculating the value of the function ( G ) when the input ( t ) equals 3. This involves replacing every instance of ( t ) in the function’s formula with 3 and simplifying the expression.", "## Step-by-Step Substitution", "Let’s begin by substituting ( t = 3 ) into the expression:", "[\nG(3) = \frac{4(3)^2 + 3}{3 - 1}\n]", "Now evaluate the expression carefully.", "### Step 1: Square the value of ( 3 )", "[\n3^2 = 9\n]", "### Step 2: Multiply by 4", "[\n4 \ imes 9 = 36\n]", "### Step 3: Add 3 to get the numerator", "[\n36 + 3 = 39\n]", "### Step 4: Simplify the denominator", "[\n3 - 1 = 2\n]", "### Step 5: Divide numerator by denominator", "[\nG(3) = \frac{39}{2} = 19.5\n]", "## Final Answer", "[\n\boxed{G(3) = 19.5}\n]", "## Why This Matters", "Knowing how to compute ( G(3) ) or any specific value is essential in many fields such as economics, engineering, and statistics, where functions model relationships between variables. Quick and accurate substitution ensures reliable outcomes, whether you’re analyzing trends, solving equations, or building predictive models.", "---", "### Quick Recap: Evaluating ( G(3) )", "- Start with: ( G(t) = \frac{4t^2 + 3}{t - 1} )\n- Substitute ( t = 3 ): ( G(3) = \frac{4(3)^2 + 3}{3 - 1} )\n- Compute: ( \frac{4 \cdot 9 + 3}{2} = \frac{36 + 3}{2} = \frac{39}{2} = 19.5 )", "Mastering this process translates to stronger mathematical fluency — a key component in academic success and real-world problem solving.", "If you found this guide helpful, share it to help others learn how to find function values effortlessly!"]
