Exploring Composition of Functions in Algebra Two

The video tutorial covers the concept of function composition, explaining how to combine two functions by plugging one into the other. It provides examples using different functions and demonstrates the importance of order in composition. The tutorial also explores real-world applications, such as currency conversion, and guides viewers in creating formulas for efficient calculations.

What does it mean to compose two functions?

• To add two functions together

• To subtract one function from another

• To multiply two functions

• To put one function inside another

If f(x) = x - 2 and g(x) = x^2, what is f(g(3))?

• 7

• 9

• 5

• 11

In the example where f(x) = x - 2 and g(x) = x^2, what is g(f(5))?

• 7

• 9

• 25

• 3

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

• 2

• 1

• 0

• -1

What is the simplified form of f(g(x)) if f(x) = x + 1 and g(x) = 2 - 3x?

• 2 - 3x + 1

• 3 - 3x

• 1 - 3x

• 2 - 3x

What is the simplified form of g(f(x)) if f(x) = x + 1 and g(x) = 2 - 3x?

• 2 - 3(x + 1)

• 2 - 3x + 1

• 2 - 3x

• 2 - 3x - 3

Why is function composition useful in real-world applications?

• It simplifies complex calculations

• It helps in converting units or currencies

• All of the above

• It allows for the combination of different functions

If f(x) converts Canadian dollars to American dollars and g(x) converts American dollars to Mexican pesos, what is g(f(5)) if f(x) = 0.76x and g(x) = 20.41x?

• 3.8

• 204.1

• 62.05

• 15.5

What is the formula for converting Canadian dollars directly to Mexican pesos using f(x) = 0.76x and g(x) = 20.41x?

• 0.76x

• 15.5x

• 20.41x

• 62.05x

What is the result of g(f(4)) if f(x) = 0.76x and g(x) = 20.41x?

• 62.05

• 3.04

• 15.5

• 204.1