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 rearranging the equation and solving for x. Next, he explains how to solve the composite function f(g(x)) by substituting g(x) into f(x). The tutorial continues with solving f(g(-3)) by substituting -3 into the composite function. The video concludes with a summary and contact information for further inquiries.

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 4 from both sides

• Divide by 2

• Cross multiply

• Add 3 to both sides

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

• x + 3

• x - 3

• 4x - 3

• 4x + 3

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

• The sum of f and g

• The product of f and g

• The composition of f and g

• The difference of f and g

How do you find f(g(x)) if f(x) = (x - 3) / 4 and g(x) = 2x + 1?

• Subtract g(x) from f(x)

• Multiply f(x) by g(x)

• Add f(x) and g(x)

• Replace x in f(x) with 2x + 1

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

• (2x - 2) / 4

• (2x + 2) / 4

• (2x + 3) / 4

• (2x - 3) / 4

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

• Evaluate g at f(-3)

• Evaluate f at g(-3)

• Evaluate g at -3

• Evaluate f at -3

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

• 2

• -1

• 0

• -2

Where can you find more resources related to the video content?

• On the instructor's Facebook page

• On the instructor's Twitter

• In the comments section

• In the video description