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:

📰 Dog Clip Art That’s Perfect for Social Media & Printables – Don’t Miss These! 📰 Transform Your Printables with These Stunning Dog Clip Art Graphics! 📰 Dogs in Clip Art: Cutest Vec Parts That Style Your Designs Instantly! 📰 Random Guid 4305747 📰 Video Gamers Developers Hyper V In Windows 10 Makes Virtualizing A Breeze 4565215 📰 Victoria Show Episodes 4742811 📰 Java Pattern 184834 📰 Sarah And Angelina Grimke 589965 📰 Cant Track Your Doordash Delivery Heres The Secret Trick Thatll Kill Your Waiters App Confidence 820477 📰 You Wont Believe How Addictive Play Sprunki Ishit Play Now 2280236 📰 The Secret Lost World Behind Miasoretyyou Wont Believe What Youll Find Inside 282482 📰 Under Salt Marsh 7623196 📰 Solaan To Usd 3054428 📰 Puerto Rico Flight 4262410 📰 Hipaa Compliance Paper Medical Records What Your Doctors Files Really Hide 5675276 📰 Edge Up Your Game Grab The Batman Costume Adults Wont Stop Talking About 5936215 📰 Define Pursuant 6264866 📰 Unlock Creativity Download The Hottest Ipad Coloring Sheets For Instant Fun 5374155

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.