Function Inverses and Compositions

In this video tutorial, Jacob Z Chamber explains how to solve mathematical problems involving functions. The video covers finding the inverse of a function, composing two functions, and evaluating the composition for a specific value. Jacob provides a detailed step-by-step explanation for each problem, ensuring viewers understand the process. The tutorial concludes with contact information and an invitation to subscribe for more content.

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?

• Divide by 2

• Add 3 to both sides

• Replace f(x) with y

• Multiply by 4

After replacing f(x) with y, what is the next step to find the inverse?

• Divide by 3

• Add 5

• Cross multiply

• Subtract 2

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 functions?

• The composition of f and g

• The difference of f and g

• The sum of f and g

• The product of f and g

How do you substitute g(x) into f(x) for f(g(x))?

• Subtract g(x) from f(x)

• Add g(x) to f(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?

• 2x + 3

• 2x + 2

• 2x - 2

• 2x - 3

What does f(g(-3)) mean?

• Multiply f(x) by -3

• Subtract -3 from g(x)

• Add -3 to f(x)

• Evaluate f(g(x)) at x = -3

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

• -2

• 0

• 2

• -4

What is the main purpose of the video?

• To teach calculus

• To explain function inverses and compositions

• To solve algebraic equations

• To introduce trigonometry