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:

📰 texas roadhouse free veterans meal 2025 📰 vincent lanking 📰 sophie cunningham injury news 📰 Master Microsoft Forms Dropdown Lists Like A Pro Heres Its Hidden Power 5816170 📰 Cam Skattebo Draft 4089390 📰 Wistorias Wand And Sword Season 2 Will Redefine Epic Battles Dont Miss It 7825471 📰 Desi Cinema App 5612736 📰 College Football 26 Team Builder 3794374 📰 Stop Getting Paid Latediscover The True Power Of Payroll Software 6356401 📰 Epstien List 7371931 📰 How Zeitweit Systems Mischa Jung Made Her Solo Debut After 15 Years With A New Vision 6993514 📰 Natura Skin Tag Remover 2992395 📰 What Actually Is Restricted Stock Dont Miss These Surprising Details 3893048 📰 Drinks Containing Gin 5751578 📰 Unlock Hidden Moves Master Ninja Parkour Multiplayer Finally 5644071 📰 When Did Hard Rock Cafe Close In Indianapolis 939853 📰 How To Block No Caller Id Calls On Iphone 9222483 📰 Batman 2Nd 2626712

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.