Exploring Composition of Functions

The video tutorial introduces the concept of composition of functions, explaining it as plugging one function into another. It covers the interpretation of composition symbols and provides examples, such as F of G of negative 5 and F of G of X plus 1, demonstrating how to solve them step-by-step. The tutorial concludes with practice problems to reinforce understanding.

What does the composition of functions generally involve?

• Multiplying two functions together

• Adding two functions together

• Dividing one function by another

• Plugging one function into another

If f(x) = x - 3, what is f(5)?

• 3

• 5

• 2

• 8

What symbol is used to denote the composition of functions?

• A plus sign

• A small circle

• A division sign

• A multiplication sign

How do you interpret f(g(-5))?

• Multiply f and g(-5)

• Add f and g(-5)

• Plug f into g(-5)

• Plug g(-5) into f

If g(x) = x^2, what is g(-5)?

• 25

• -5

• -25

• 5

Given f(x) = x - 2 and g(x) = x^2, what is f(g(-5))?

• 25

• 21

• 27

• 23

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

• x - 2

• x^2 + 2

• x^2 - x

• x^2 - 2

What is the result of (x + 1)^2?

• x^2 + 1

• x^2 + 2x + 1

• x^2 + 2x

• x^2 - 1

If f(x) = x - 2 and g(x) = x^2, what is f(g(x + 1))?

• x^2 - 2x - 1

• x^2 - 2x + 1

• x^2 + 2x + 1

• x^2 + 2x - 1

What is the simplified form of (x - 1)^2?

• x^2 + 2x - 1

• x^2 + 1

• x^2 - 2x + 1

• x^2 - 1