Given \( f(x) = 3x + 2 \) and \( g(x) = x^2 - 1 \), compute \( g(f(3)) \).
["Compute ( g(f(3)) ) Fast and Accurately: A Step-by-Step Guide", "When working with composite functions in algebra, understanding how to evaluate expressions like ( g(f(3)) ) is essential. In this article, we’ll break down the computation of ( g(f(3)) ) using the given functions:\n[ f(x) = 3x + 2 ]\n[ g(x) = x^2 - 1 ]", "Step 1: Evaluate the Inner Function ( f(3) )\nFirst, substitute ( x = 3 ) into ( f(x) ):\n[\nf(3) = 3(3) + 2 = 9 + 2 = 11\n]", "Step 2: Use the Result as Input for ( g(x) )\nNow that we know ( f(3) = 11 ), we substitute this into ( g(x) ):\n[\ng(f(3)) = g(11)\n]", "Step 3: Compute ( g(11) )\nUsing the definition of ( g(x) = x^2 - 1 ):\n[\ng(11) = 11^2 - 1 = 121 - 1 = 120\n]", "Final Answer:\n[\ng(f(3)) = 120\n]", "This calculation demonstrates a key concept in function composition: substitute step-by-step, starting from the innermost function. Mastering such steps helps students and learners confidently solve more complex function problems and improve their algebraic problem-solving skills.", "If you're studying functions, practice with composite expressions like ( g(f(x)) ) and ( g(f(g(x))) )—they’re foundational in calculus, applied math, and computer science!", "---", "Keywords:\n( g(f(3)) ), function composition, evaluate composite functions, ( f(x) = 3x + 2 ), ( g(x) = x^2 - 1 ), step-by-step solution, algebra tutorial, math problem-solving, conditional functions", "Meta Description:\nLearn how to compute ( g(f(3)) ) step-by-step with ( f(x) = 3x + 2 ) and ( g(x) = x^2 - 1 ). A clear, educational guide for students and math enthusiasts."]
