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:

📰 5Question: A bioinformatician is aligning sequences from three different species, each contributing exactly 3 unique genetic markers. If the markers within each species are indistinguishable, but markers from different species are distinguishable, how many distinct sequences can be formed by arranging all 9 markers in a line? 📰 Solution: We are arranging 9 genetic markers in a line, where there are 3 indistinguishable markers from species A, 3 from species B, and 3 from species C. Since markers from the same species are indistinguishable, the number of distinct arrangements is given by the multinomial coefficient: 📰 rac{9!}{3! \cdot 3! \cdot 3!} = rac{362880}{6 \cdot 6 \cdot 6} = rac{362880}{216} = 1680 📰 Unbelievable Secrets Hidden Inside The Tower Of Power 📰 Unbelievable Secrets Hidden Inside This Panel Ready Refrigerator 📰 Unbelievable Secrets Hidden Inside Your Propane Fire Pit Everyone Suspected This Burn 📰 Unbelievable Secrets Inside Every Ping Pong Ball Youve Missed 📰 Unbelievable Secrets Panoxyl Patch Secrets Revealed 📰 Unbelievable Survival Secret Pads With Wings That Defy Reality 📰 Unbelievable Trick To Instantly Boost Your Energy Fast With Pizzarella Plus 📰 Unbelievable Truth About Ops In Baseball No One Wants To Know 📰 Unbelievable Truths Hiding In Psalm 51 Kjv You Cant Ignore 📰 Unchseen Moments Of Passion Nude Old Women Defying Taboo In Breathtaking Private Shots 📰 Uncommanded Storms Consolidating Extreme Weather Hits Without Warning 📰 Uncover Hollywood Style Plus Size Wedding Guest Dresses That Turn Heads 📰 Uncover How Privacy Trees Are Changing How We Protect Personal Space Forever 📰 Uncover The Best Pink Gemstones That Can Change Your Life Before Anyone Else 📰 Uncover The Hidden Scare Inside Every Pumpkinno Cost Just Complete Panic

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.