Function Composition and Applications

The video tutorial explores the concept of function composition, starting with an introduction to the problems that lead to composing functions. It explains the composition of functions with examples, demonstrating how to solve real-world problems like calculating sales commissions and discounts using function composition. The tutorial provides step-by-step examples to illustrate the process and emphasizes the importance of understanding the inner and outer functions in composition.

What is the primary reason for using function composition?

• To simplify complex functions

• To avoid using functions altogether

• To increase the number of variables

• To make functions more difficult

If f(x) = P and g(x) = Q, what is f(g(x)) equal to?

• g(Q)

• f(P)

• g(P)

• f(Q)

In the example where f(x) = 3x + 2 and g(x) = 4x, what is f(g(x))?

• 4x + 2

• 12x + 2

• 12x + 8

• 3x + 8

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

• 4x + 2

• 3x + 8

• 12x + 2

• 12x + 8

How do you calculate f(g(3)) when f(x) = 3x + 2 and g(x) = 4x?

• 36

• 38

• 40

• 34

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

• 2

• 0

• -2

• -4

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

• 12x + 2

• 12x + 8

• 3x + 8

• 4x + 2

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

• 12x + 8

• 4x + 2

• 3x + 8

• 12x + 2

How do you calculate f(g(3)) when f(x) = 3x + 2 and g(x) = 4x?

• 40

• 36

• 34

• 38

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

• -4

• -2

• 0

• 2