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:

📰 What your irri sys is hiding that’s changing how you drive forever 📰 Ever wonder what irri sys really tracks—shocking truth uncovered 📰 Your irri system doesn’t lie—this vital data flavor changes everything 📰 You Wont Stop Watchingnicklars Hidden Action Exposes The Truth Forever 📰 You Wont Throw Out Your Macbook When It Turns Orangeheres Whats Really Happening 📰 You Wont Trust What Lurks Inside The Secret Natural Bridge Zoo 📰 You Wont Understand What Oshinko Roll Does To Your Taste Until Now 📰 You Wouldnt Guess What Small Amounts Of Old Bay Unlock In Your Familys Recipes 📰 Youd Never Admit Itbut Your Muffin Top Demands Attention 📰 Youd Never Expect This Otterbox Warranty Trap Discover The Hidden Risk Inside 📰 Youll Crawl For This Oakley Backpack Hidden In Plain Sight 📰 Youll Cry When You See This Mysterious Filmplakat Revealed 📰 Youll Never Believe How Deep The Truth Really Runs Behind Your Thoughts 📰 Youll Never Believe How Easy Mini Split Installation Really Is 📰 Youll Never Believe How Many Ounces Fit In A Half Gallonby A Half 📰 Youll Never Believe How My Pianos First Note Set My Soul Freewhat It Did To Me 📰 Youll Never Believe How This Oil Pan Transformed My Engines Performance 📰 Youll Never Believe This Hidden Nyc Side Parking Hack

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.