Question: If $ f(x) = 3x - 7 $ and $ g(x) = x^2 + 2x $, what is $ g(f(4)) $?

How to Calculate $ g(f(4)) $: A Step-by-Step Guide for Function Composition

Understanding function composition is a fundamental skill in algebra, especially when working with expressions like $ f(x) = 3x - 7 $ and $ g(x) = x^2 + 2x $. One common question that arises is: If $ f(x) = 3x - 7 $ and $ g(x) = x^2 + 2x $, what is $ g(f(4)) $?

This article walks you through the entire process clearly and efficiently, helping you master evaluating composite functions.

Understanding the Context

What Is Function Composition?

Function composition involves plugging the output of one function into another. The notation $ g(f(x)) $ means you first apply function $ f $ to $ x $, then take that result and apply function $ g $ to it.

In this case, we need to compute $ g(f(4)) $, which requires two key steps:

Evaluate $ f(4) $
Use that result as the input to $ g(x) $

Question: If $ f(x) = 3x - 7 $ and $ g(x) = x^2 + 2x $, what is $ g(f(4)) $?

Key Insights

Step 1: Evaluate $ f(4) $

Given:
$$
f(x) = 3x - 7
$$

Substitute $ x = 4 $:
$$
f(4) = 3(4) - 7 = 12 - 7 = 5
$$

So, $ f(4) = 5 $

🔗 Related Articles You Might Like:

📰 How An Unpolished Team Turned Simple Kick Into Pure Magic 📰 Discover The Wild Ambition Of An Amateur Football Combination No One Saw Coming 📰 Amateurs Teach the World What They Learned—Shocking Secrets Exposed! 📰 Learn Open G Tuning Now The Ultimate Guide For Rock Guitarists 📰 Learn The Surprising Way To Say No In In Sign Language Today 📰 Left Brain Hacks And Hidden Secrets Inside The Nintendo 3Ds Xl Fact File 📰 Legacy In A Fur Layer Discover The Storied World Of Old English Bulldogs 📰 Legacy 📰 Legendary Pac Man Ghosts Why Every Fan Still Wins Theyre Obsessed With 📰 Length 3W 24 📰 Leont Miss This The Secret Paladin Meaning Thats Changing How We See Knights Forever 📰 Les Deux Permettent 4 Lots Donc Le Total Est De 4 5 20 Moles De Produit C 📰 Les Dimensions Sont De 30 Mtres Par 15 Mtres 📰 Les Nombres Sont 10 Et 12 📰 Let A 4X B 2X 📰 Let A 9 C 15 Solve For B 92 B2 152 📰 Let D Gcdp Q Then P Dk Q Dl With Gcdk L 1 And 📰 Let N 100A 10B 3 We Require N Equiv 0 Pmod9 Since 100 Equiv 1 Pmod9 10 Equiv 1 Pmod9 So

Final Thoughts

Step 2: Evaluate $ g(f(4)) = g(5) $

Now use the result from Step 1. Since $ g(x) = x^2 + 2x $, substitute $ x = 5 $:
$$
g(5) = 5^2 + 2(5) = 25 + 10 = 35
$$

Final Answer

Putting it all together:
$$
g(f(4)) = g(5) = 35
$$

Why This Matters: Function Composition in Math and Beyond

Function composition is not just a theoretical concept — it appears in chemistry, economics, computer science, and engineering. For example, if $ f(x) $ models a price increase and $ g(x) $ represents tax calculation, then $ g(f(x)) $ combines both steps sequentially.

Mastering these principles helps build problem-solving skills essential in higher mathematics, programming, and real-world modeling.