Exploring Composite Functions in Mathematics

The video tutorial explains composite functions, focusing on finding f(g(x)) and g(f(x)). It begins with a definition of functions and composite functions, followed by a step-by-step guide to solving them. Examples are provided using specific functions, and solutions are verified with real numbers. The video concludes with a practice question for viewers.

What is a composite function?

• A function that maps multiple inputs to one output

• A function that has no inputs

• A function that is formed by combining two functions

• A function that maps one input to multiple outputs

What is the first step in finding a composite function?

• Substitute the outer function

• Substitute the inner function

• Simplify the outer function

• Combine the functions directly

What is the inner function in f(g(x)) if f(x) = 3x - 1 and g(x) = x^2 - 2?

• 3x - 1

• g(x)

• x^2 - 2

• f(x)

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

• 3x^2 - 7

• 3x^2 - 2

• 3x^2 - 6

• 3x^2 - 1

What is the inner function in g(f(x)) if f(x) = 3x - 1 and g(x) = x^2 - 2?

• x^2 - 2

• g(x)

• f(x)

• 3x - 1

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

• 9x^2 - 6x + 2

• 9x^2 - 6x - 2

• 9x^2 - 6x - 1

• 9x^2 - 6x + 1

What is the output of g(-2) if g(x) = x^2 - 2?

• -2

• 0

• 4

• 2

What is the output of f(2) if f(x) = 3x - 1?

• 7

• 5

• 4

• 6

What is the output of f(-2) if f(x) = 3x - 1?

• -6

• -7

• -5

• -8

What is the output of g(-7) if g(x) = x^2 - 2?

• 45

• 50

• 49

• 47