Function Composition and Inverses

In this video tutorial, Jacob Z Chamber explains how to solve mathematical problems involving functions. The video begins with an introduction to the functions f(x) and g(x). Jacob then demonstrates how to find the inverse of f(x) by making x the subject of the formula. Next, he explains how to compose the functions to find f(g(x)) and evaluates f(g(-3)) using the results from the previous steps. The video concludes with a call to action to subscribe and contact information for further engagement.

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?

• Add 5

• Divide by 3

• Switch x and y

• Multiply by 2

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

• Subtract 3 from both sides

• Add 3 to both sides

• Divide by 2

• Multiply by 4

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 sum of f and g

• The product of f and g

• g applied to the result of f(x)

• f applied to the result of g(x)

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

• Divide f(x) by g(x)

• Multiply f(x) by g(x)

• Add g(x) to f(x)

• Replace x in f(x) 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 + 5) / 4

What is the value of f(g(-3))?

• -2

• 0

• -1

• 2

What is the first step in evaluating f(g(-3))?

• Add 3 to -3

• Substitute -3 into g(x)

• Multiply -3 by 2

• Divide -3 by 4

What is the final result of f(g(-3)) after simplification?

• 1

• -2

• 0

• -1