To find \(f(2)\) for the function \(f(x) = 2x^3 - 5x^2 + 3x - 1\), substitute \(x = 2\) into the expression:

["# How to Find ( f(2) ) for the Function ( f(x) = 2x^3 - 5x^2 + 3x - 1 )", "Understanding how to evaluate a function at a specific input is a fundamental skill in algebra and calculus. Whether you’re solving equations, analyzing data, or working on advanced math problems, knowing how to compute ( f(2) ) for a given function is essential. In this article, we’ll walk through step-by-step how to find ( f(2) ) for the cubic polynomial:", "[\nf(x) = 2x^3 - 5x^2 + 3x - 1\n]", "## What Does ( f(2) ) Mean?", "When we write ( f(2) ), we are asking: What is the output of the function when the input is 2? To find this value, we substitute ( x = 2 ) into the function and simplify using the order of operations (PEMDAS/BODMAS).", "## Step-by-Step Substitution", "Substitute ( x = 2 ) into the expression:", "[\nf(2) = 2(2)^3 - 5(2)^2 + 3(2) - 1\n]", "Now compute each term carefully:", "1. Evaluate the exponent first:\n[\n2^3 = 8\n]\nSo:\n[\n2(2)^3 = 2 \ imes 8 = 16\n]", "2. Next, the squared term:\n[\n2^2 = 4\n]\nThen multiply by (-5):\n[\n-5(4) = -20\n]", "3. Linear term:\n[\n3(2) = 6\n]", "4. Constant term remains:\n[\n-1\n]", "Now add all the computed values together:", "[\nf(2) = 16 - 20 + 6 - 1\n]", "### Simplify the expression step-by-step:", "[\n16 - 20 = -4\n]\n[\n-4 + 6 = 2\n]\n[\n2 - 1 = 1\n]", "## Final Result", "[\nf(2) = 1\n]", "So, evaluating the function at ( x = 2 ), we find that ( f(2) = 1 ).", "---", "This simple substitution method applies to polynomial, rational, and many other types of functions. Mastering it builds a strong foundation for advanced math and problem-solving skills.", "### Pro Tip for Efficiency", "When computing ( f(a) ), write clearly and compute powers and products first before combining like terms — this minimizes errors and keeps your work organized.", "---", "Keywords: ( f(2) ), function evaluation, mathematical computation, algebra tips, how to compute f(2), step-by-step solution, polynomial function, cubic function, math tutorial."]