Question: What is $ f(g(2)) $ if $ f(x) = x^2 - 4x + 5 $ and $ g(x) = 3x - 1 $? - Midis
Understanding $ f(g(2)) $: A Step-by-Step Solution Using Functions $ f(x) = x^2 - 4x + 5 $ and $ g(x) = 3x - 1 $
Understanding $ f(g(2)) $: A Step-by-Step Solution Using Functions $ f(x) = x^2 - 4x + 5 $ and $ g(x) = 3x - 1 $
Ever encountered the expression $ f(g(2)) $ and wondered how to evaluate it? Whether you're a student learning function composition or simply curious about working with mathematical functions, solving $ f(g(2)) $ involves two key steps: first, evaluate the inner function $ g(2) $, then use that result as the input for $ f $. In this article, we break down how to compute $ f(g(2)) $ using the specific functions $ f(x) = x^2 - 4x + 5 $ and $ g(x) = 3x - 1 $, making it easier to understand sequence and function operations.
Understanding the Context
What Does $ f(g(2)) $ Mean?
Function composition, denoted $ f(g(x)) $, means applying the function $ g $ first, then applying $ f $ to the result. So $ f(g(2)) $ means plug $ g(2) $ into $ f $. Follow these steps:
- Evaluate $ g(2) $
- Plug the result into $ f $
- Simplify to find $ f(g(2)) $
Key Insights
Step 1: Calculate $ g(2) $
Given:
$ g(x) = 3x - 1 $
Substitute $ x = 2 $:
$ g(2) = 3(2) - 1 = 6 - 1 = 5 $
Step 2: Evaluate $ f(5) $
🔗 Related Articles You Might Like:
📰 How the Rook Kast Strategy Won 10,000 Games Online – Shocking Results! 📰 The Hidden Rook Kast Trick You’re Not Supposed to Know – Pro Gamers Swear By It! 📰 Rook Kast Secrets: Why This Move Destroys Opponents in Milliseconds! 📰 You Wont Believe How Easy Slow Cooker Short Ribs Are To Maketasty Stew In Under 8 Hours 📰 You Wont Believe How Easy Sourdough Discard Pizza Dough Is To Maketry It Today 📰 You Wont Believe How Easy These Small Box Braids Looktry Them Today 📰 You Wont Believe How Epic This Soccer Anime Scene Getswatch Now 📰 You Wont Believe How Every Spiderman Character Survived A Dangerous Battle 📰 You Wont Believe How Evil Spider Gwen Really Is Shell Shock You 📰 You Wont Believe How Fast Sonic 3 Air Blasts100 Must Have Speed Tech 📰 You Wont Believe How Fast Sonra Build Outperforms All Other Setups 📰 You Wont Believe How Fast The 2015 Sonata Acceleratesgas Station Shocked Me 📰 You Wont Believe How Fast The Sonic 3 Paramount Plus Isthis Speed Machine Shocked Everyone 📰 You Wont Believe How Fast Your Xbox Speedtest Originally Loaded Heres What Happened 📰 You Wont Believe How Hard Space Invaders Istry It Before Its Too Late 📰 You Wont Believe How Hidden Snipe Mha Gameplay Explosively Boosts Your Strategy 📰 You Wont Believe How Hidden The Family Secrets In Spy X Family Really Are 📰 You Wont Believe How Hidden This Skeleton Face Paint Looks When It GlowsFinal Thoughts
Now that we know $ g(2) = 5 $, compute:
$ f(x) = x^2 - 4x + 5 $
So,
$ f(5) = (5)^2 - 4(5) + 5 = 25 - 20 + 5 = 10 $
Final Result: $ f(g(2)) = 10 $
Thus, $ f(g(2)) = 10 $ is the final value.
Why Understanding Function Composition Matters
Function composition $ f(g(x)) $ is fundamental in algebra, calculus, and applied mathematics. It models real-world scenarios where one process depends on another — such as transforming data through successive operations. Understanding how to decompose $ f(g(x)) $ into manageable steps strengthens your problem-solving skills and prepares you for advanced topics.
Summary
- $ g(x) = 3x - 1 $
- $ g(2) = 5 $
- $ f(x) = x^2 - 4x + 5 $
- $ f(5) = 10 $
- Therefore, $ f(g(2)) = 10 $
