g(a)=3a+2, f(a)=2a-4; Find (g/f)(3)

Summary

In the 'Minute Math' video, Sean Gann teaches function operations by solving the problem of finding \( g \over f \) of 3. The functions given are \( g(a) = 3a + 2 \) and \( f(a) = 2a - 4 \). Sean demonstrates how to divide the functions, substitute '3' for 'a', and simplify to get the final answer of \( \frac{11}{2} \). The video is designed to help viewers understand function operations and encourages them to engage with the channel for more free math lessons.

Takeaways

• 📘 Sean Gann introduces the topic of function operations in the video.
• 🔢 The functions g(a) = 3a + 2 and f(a) = 2a - 4 are given as part of the problem.
• 📌 The task is to find the value of g(a) / f(a) when a = 3.
• 🧮 To solve, Sean demonstrates the process of dividing g(a) by f(a).
• ➡️ Substituting 'a' with 3, the expression becomes (3*3 + 2) / (2*3 - 4).
• 📈 Simplifying the expression, the numerator becomes 11 and the denominator becomes 2.
• 📉 The final result of g(3) / f(3) is 11/2.
• 🎓 The video aims to educate viewers on how to perform operations on functions.
• 📈 Sean encourages viewers to subscribe and like the video for more free math lessons.
• 👨‍🏫 Minute Math is portrayed as a helpful resource for those needing math assistance.

Q & A

What is the main topic of the Minute Math video presented by Sean Gann?

The main topic of the video is function operations, specifically focusing on finding the value of g over f of a given number.

What are the given functions in the problem presented in the video?

The given functions are g(a) = 3a + 2 and f(a) = 2a - 4.

What does the video aim to calculate?

The video aims to calculate the value of g over f when a is substituted with 3, i.e., g(f(3)) or g(3)/f(3).

How does the video simplify the expression for g over f of a?

The video simplifies the expression by substituting g(a) with 3a + 2 and f(a) with 2a - 4, and then dividing the two expressions.

What is the first step Sean takes to solve the problem?

The first step Sean takes is to substitute the value of 'a' with 3 in the expressions for g(a) and f(a) to find g(f(3)) or g(3)/f(3).

What is the value of g(3) according to the video?

The value of g(3) is calculated as 3*3 + 2, which simplifies to 9 + 2, resulting in 11.

What is the value of f(3) as shown in the video?

The value of f(3) is calculated as 2*3 - 4, which simplifies to 6 - 4, resulting in 2.

What is the final simplified result for g over f of 3 as presented in the video?

The final simplified result for g over f of 3 is 11/2.

What is the purpose of the video according to the closing remarks?

The purpose of the video is to provide free math lessons to help viewers when they need assistance with mathematics.

How does Sean encourage viewers to support the channel at the end of the video?

Sean encourages viewers to support the channel by subscribing and liking the video, which helps in creating more free math lessons.