Finding Composite Functions with Numbers

This video tutorial explains composite functions, focusing on finding f(g(x)) and g(f(x)) using specific examples. It begins with an introduction to composite functions and their significance, followed by a detailed definition and domain explanation. The video then provides step-by-step solutions for example problems involving f(g(x)) and g(f(x)) when x equals 3. The tutorial concludes with encouragement for viewers to practice and review their understanding.

What is a composite function?

• A function that combines two functions

• A function that maps one input to multiple outputs

• A function that maps multiple inputs to one output

• A function that only works with numbers

What is the largest turtle mentioned in the video?

• Hawksbill sea turtle

• Loggerhead sea turtle

• Leatherback sea turtle

• Green sea turtle

What is the domain of a composite function f(g(x))?

• The set of all x in the domain of g

• The set of all x in the domain of f

• The set of all x in the domain of g such that g(x) is in the domain of f

• The set of all x in the domain of f such that f(x) is in the domain of g

What is the first step in solving a composite function?

• Substitute the outer function

• Simplify the expression

• Substitute the inner function

• Follow the order of operations

What is f(g(3)) if f(x) = x^2 and g(x) = 3x - 5?

• 25

• 16

• 22

• 9

What is the new input when finding f(g(3))?

• 9

• 16

• 3

• 4

What is the result of (3x - 5)^2?

• 9x^2 - 15x + 20

• 9x^2 - 30x + 20

• 9x^2 - 15x + 25

• 9x^2 - 30x + 25

What is g(f(3)) if f(x) = x^2 and g(x) = 3x - 5?

• 22

• 25

• 16

• 9

What is the new input when finding g(f(3))?

• 16

• 9

• 3

• 4

What is the result of 3(x^2) - 5?

• 3x^2 + 10

• 3x^2 + 5

• 3x^2 - 5

• 3x^2 - 10