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) $

Solved QUESTION 6 Given : F(x) = 2x2 – 3x + 5 and g(x)=x-4 | Chegg.com

Image Gallery

Solved Find the following. f(x) = 2x - 3, g(x) = 2 - x (f + | Chegg.com

Solved Find functions f and g so that h(x) = (fºg)(x). 14) | Chegg.com

4 if fx x2 gx 5x and hx x 4 find each value find hf4 2x2 7x 3 b 7x3 c ...

Solved Given f(x)=4x2 + 3x + 4 and g(x)=3x-7. find (go)(x). | Chegg.com

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:

📰 CTL Just Shocked the Market — Discover Its Stock Symbol Before Anyone Else! 📰 The Stock Symbol CTL is Hiding the Secret to Explosive Gains — Find Out Why! 📰 CTL Stock Symbol Caught Fire — Everyones Discussing This NOW! #TrendingNow 📰 Why These Oracle Com Jobs Are Fastest Growing In Techjoin Now 7818887 📰 Is Surface Pro 11 With Intel Worth The Hype Experts Reveal The Truth 6686689 📰 Ssd Definition 190606 📰 Filtration Water System 4232370 📰 Bank Of America Saturday Hours 1404138 📰 5 You Didnt Hear This 1Usd Can Buy Estimated X Nis Check Now 3849814 📰 Nvidia Price Prediction 2025 Will X Become Unthinkable Heres The Shocking Forecast 8571906 📰 Flushing Ac System 2774763 📰 Best Ai For School 4014575 📰 Can One Skylight Paycard Change Your Entire Shopping Experience Find Out Now 1603764 📰 F To Promote Horizontal Gene Transfer Between Species 7375950 📰 Samsara Stock Shock The Hidden Phenomenon Every Investor Should Know Before It Explodes 1754060 📰 Stop Trusting Stones The Diamond Tester Cracks Every Secret Inside 5848764 📰 The Avengers Earths Mightiest Heroes 4914490 📰 Cars Movie 3399814

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.