Function Composition and Domains

The video tutorial explains the concept of function composition, using notation and practical examples. It covers how to determine the domain and range of composed functions, using specific examples like f(x) = x^2 - 2x and g(x) = x + 3. The tutorial also demonstrates how to calculate compositions like H(x) and P(Q(-2)), and explores the domains of f(g(x)) and g(f(x)).

What is the notation used to represent the composition of two functions?

• A multiplication sign between the functions

• A division sign between the functions

• A degree sign between the functions

• A plus sign between the functions

In function composition, what becomes the input of the outer function?

• The difference between the inner and outer functions

• The output of the inner function

• The input of the inner function

• The sum of the inner and outer functions

What is the domain of the composition of two functions?

• The union of the domains of both functions

• The intersection of the domains of both functions

• The domain of the inner function

• The domain of the outer function

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

• x^2 - 4x + 3

• x^2 + 4x + 3

• x^2 - 2x + 3

• x^2 + 6x + 9

What is the domain of the composition f(g(x)) if both f and g have all real numbers as their domains?

• All real numbers

• Only positive numbers

• Only negative numbers

• Only integers

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

• x^2 + 4x + 3

• x^2 - 2x + 3

• x^2 - 4x + 3

• x^2 + 6x + 9

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

• Only negative numbers

• Only positive numbers

• All real numbers

• Only integers

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

• x^2 + 4x + 3

• x^2 - 4x + 3

• x^2 - 2x + 3

• x^2 + 6x + 9

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

• Only positive numbers

• All real numbers

• Only negative numbers

• Only integers

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

• x^2 + 2x + 3

• x^2 - 2x + 3

• x^2 + 3

• x^2 - 3