Substitute \(x = 3\) into the function: \(f(3) = 3^2 - 4 \times 3 + 4\).

["# Substitute (x = 3) into the Function: (f(3) = 3^2 - 4 \ imes 3 + 4)", "When analyzing mathematical functions, substitution is a fundamental operation that allows us to evaluate a function at specific input values. This article explores how to substitute (x = 3) into the expression (f(x) = 3^2 - 4 \ imes 3 + 4), breaking down each step to ensure clarity and accuracy. By understanding this process, learners and math enthusiasts can better apply substitution techniques to evaluate functions quickly and confidently.", "## Understanding the Function", "The function under consideration is:", "[\nf(x) = 3^2 - 4 \ imes 3 + 4\n]", "At first glance, the notations may appear confusing, but simplifying step-by-step helps clarify the structure:", "- The term (3^2) means (3) squared.\n- The term (-4 \ imes 3) involves multiplication: (4) times (3).\n- The last term is simply (+4).", "Note: Although written with (3) in multiple places, in function evaluation we treat (x) as a symbol plugged in with (3). The actual function form is more generally written as:", "[\nf(x) = x^2 - 4x + 4\n]", "So substituting (x = 3) means replacing every (x) with (3).", "## Substitution Step-by-Step", "To find (f(3)), perform the replacement:", "[\nf(3) = (3)^2 - 4 \ imes 3 + 4\n]", "Now simplify each term using standard order of operations (PEMDAS/BODMAS):", "1. Evaluate the exponent first:\n [\n (3)^2 = 9\n ]", "2. Perform the multiplication:\n [\n 4 \ imes 3 = 12\n ]", "3. Substitute and simplify:\n [\n f(3) = 9 - 12 + 4\n ]", "4. Perform addition and subtraction from left to right:\n [\n 9 - 12 = -3\n ]\n [\n -3 + 4 = 1\n ]", "## Final Result", "[\nf(3) = 1\n]", "This result means that when the function (f(x) = x^2 - 4x + 4) is evaluated at (x = 3), the output is (1).", "---", "### Why This Matters", "Substituting values into functions is essential in calculus, algebra, and applied mathematics. It enables:", "- Predicting outputs based on inputs\n- Finding specific function values critical in optimization problems\n- Verifying function behavior at certain points", "By mastering substitution—especially with structured expressions like (f(3))—you build a solid foundation for graphing, solving equations, and applying functions in real-world modeling.", "---", "## Tips for Efficient Substitution", "- Always start with exponents and then handle multiplications and divisions.\n- Parentheses matter—don’t omit them even if implicit.\n- Simplify step-by-step to avoid arithmetic errors.\n- Double-check each operation after substitution.", "---", "## Summary", "Substituting (x = 3) into (f(x) = 3^2 - 4 \ imes 3 + 4) yields:", "[\nf(3) = 3^2 - 4 \ imes 3 + 4 = 9 - 12 + 4 = 1\n]", "This simple evaluation illustrates a key algebraic skill with wide applications in mathematics and science.", "---", "Keywords: substitute (x = 3), evaluate function, (f(3) = 3^2 - 4 \ imes 3 + 4), function evaluation, math tutorial, algebra, calculus application, step-by-step substitution", "---", "Meta Description:\nLearn how to substitute (x = 3) into (f(x) = 3^2 - 4 \ imes 3 + 4), step-by-step simplification, and final result of 1. Perfect for students mastering function evaluation and algebra fundamentals."]