Function Inverses and Composition

In this video tutorial, Jacob Z. Chamber explains how to work with two functions, f(x) and g(x). He demonstrates how to find the inverse of f(x) by switching variables and solving for x. Next, he shows how to compose the functions to find f(g(x)) and evaluates this composition for x = -3. The video concludes with a call to action to subscribe and follow for more content.

What are the two functions introduced in the video?

• h(x) and j(x)

• g(x) and h(x)

• f(x) and g(x)

• f(x) and h(x)

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

• Divide by 3

• Add 5 to both sides

• Switch x and y

• Multiply by 2

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

• Solve for x

• Solve for y

• Subtract 3

• Multiply by 4

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

• 4x + 3

• x + 3

• x - 3

• 4x - 3

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

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

• The sum of f and g

• The product of f and g

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

How do you substitute g(x) into f(x) when finding f(g(x))?

• Replace y with g(x)

• Replace g with f(x)

• Replace x with g(x)

• Replace f with 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 g at 3 and then f at the result

• Evaluate f at -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?

• 0

• 2

• -2

• -1

What is the main purpose of the video?

• To teach how to solve quadratic equations

• To introduce calculus concepts

• To explain the concept of function inverses and composition

• To demonstrate graphing techniques