Function Composition and Inverses

In this video, Jacob Z Chamber explains how to solve problems involving functions, specifically focusing on finding the inverse of a function and solving composite functions. The tutorial begins with an introduction to the problem, followed by a detailed walkthrough of finding the inverse of f(x). Next, Jacob demonstrates how to solve f(g(x)) and then applies this to find f(g(-3)). The video concludes with a summary and contact information for further assistance.

What are the two functions introduced in the video?

• f(x) and h(x)

• f(x) and g(x)

• g(x) and h(x)

• h(x) and j(x)

What is the first step in finding the inverse of a function?

• Add 3 to both sides

• Switch x and y

• Divide by 4

• Multiply by 2

After switching x and y, what is the next step to find the inverse of f(x)?

• Make x the subject of the formula

• Multiply by 4

• Subtract 3 from both sides

• Add 3 to both sides

What is the inverse of f(x) if f(x) = (x - 3) / 4?

• 4x - 3

• x + 3

• 4x + 3

• x - 3

What does f(g(x)) represent in terms of function composition?

• The function g applied to the result of f(x)

• The function f applied to the result of g(x)

• The product of f(x) and g(x)

• The sum of f(x) and g(x)

How do you substitute g(x) into f(x) to find f(g(x))?

• Add g(x) to f(x)

• Divide f(x) by g(x)

• Replace x in f(x) with g(x)

• Multiply f(x) by g(x)

What is the result of f(g(x)) if g(x) = 2x + 1 and f(x) = (x - 3) / 4?

• (2x + 1 - 3) / 4

• (2x + 3) / 4

• (2x + 1) / 4

• (2x - 1) / 4

What does f(g(-3)) mean in terms of function evaluation?

• Evaluate both f and g at -3

• Evaluate g at f(-3)

• Evaluate g at -3 and then f at the result

• Evaluate f at -3

What is the result of f(g(-3)) if g(x) = 2x + 1 and f(x) = (x - 3) / 4?

• -2

• 2

• -1

• 0

What is the main takeaway from the video?

• Understanding how to add functions

• Graphing linear functions

• Solving quadratic equations

• Learning to find inverses and compose functions