Question: Let $f(x) = 2x^2 - 3x + 1$ and $g(x) = \sqrt{x + 4}$. What is $g(f(2))$?

["Understanding $g(f(2))$: Step-by-Step Calculation with $f(x) = 2x^2 - 3x + 1$ and $g(x) = \sqrt{x + 4}$", "Understanding how to evaluate composed functions is essential in algebra and calculus. One common question is: What is $g(f(2))$ when $f(x) = 2x^2 - 3x + 1$ and $g(x) = \sqrt{x + 4}$? This article explains how to solve this step-by-step, making it easier to master function composition.", "---", "### Step 1: Evaluate $f(2)$", "The first step in finding $g(f(2))$ is to compute $f(2)$. Given:", "$$\nf(x) = 2x^2 - 3x + 1\n$$", "Substitute $x = 2$:", "$$\nf(2) = 2(2)^2 - 3(2) + 1 = 2(4) - 6 + 1 = 8 - 6 + 1 = 3\n$$", "So, $f(2) = 3$.", "---", "### Step 2: Substitute $f(2)$ into $g(x)$", "Now, use this result as the input for $g(x)$:", "$$\ng(x) = \sqrt{x + 4}\n$$", "Since $f(2) = 3$, compute $g(f(2)) = g(3)$:", "$$\ng(3) = \sqrt{3 + 4} = \sqrt{7}\n$$", "---", "### Final Result", "$$\ng(f(2)) = \sqrt{7}\n$$", "---", "### Why This Matters (SEO Keywords Focus)", "Understanding function composition like $g(f(2))$ helps students and professionals in mathematics, programming, and engineering. Key SEO terms associated with this topic include:\n- Function composition\n- Evaluate $g(f(x))$ step-by-step\n- Solve $g(f(2))$ algebraically\n- Step-by-step quadratic function evaluation\n- Apply $f(x)$ followed by $g(x)$\n- Difference $g(f(x))$ at a point", "Perfecting such problems builds problem-solving confidence and is valuable for exams, coding logic, and advanced math applications.", "Summary:\nGiven $f(x) = 2x^2 - 3x + 1$ and $g(x) = \sqrt{x + 4}$,\n$$\ng(f(2)) = \sqrt{7}\n$$", "---", "Try similar problems: Compute $g(f(0))$, $g(f(-1))$, or explore how changing $f(x)$ affects $g(f(x))$. Practice makes perfect!"]