Function Composition and Decomposition

Mr. Potter explains compositions of functions, covering how to combine functions through addition, subtraction, multiplication, and division. He delves into true composition, domain restrictions, and evaluates compositions using algebraic, tabular, and graphical methods. The lesson concludes with decomposition of complex functions into simpler parts.

What is the result of adding the functions f(x) = x^2 - 4 and g(x) = 2x + 3?

• x^2 + 2x + 7

• x^2 + 2x - 1

• x^2 - 2x - 1

• x^2 - 2x + 7

When subtracting g(x) from f(x), what is the result if f(x) = x^2 - 4 and g(x) = 2x + 3?

• x^2 + 2x - 7

• x^2 - 2x - 7

• x^2 - 2x + 7

• x^2 + 2x + 7

How does the order of subtraction affect the result of f(x) - g(x) and g(x) - f(x)?

• The results are identical

• The results are the same

• The results are opposites

• The results are unrelated

What is the product of f(x) = x^2 - 4 and g(x) = 2x + 3?

• 2x^3 + 3x^2 - 8x + 12

• 2x^3 - 8x - 3x^2 + 12

• 2x^3 - 8x + 3x^2 - 12

• 2x^3 + 3x^2 - 8x - 12

What must be considered when dividing functions f(x) and g(x)?

• The sum of the functions

• The product of the functions

• Domain restrictions

• The difference of the functions

What is the domain restriction for f(x)/g(x) if g(x) = 2x + 3?

• x cannot be -2

• x cannot be 2

• x cannot be -3/2

• x cannot be 0

In a true composition of functions, what does f(g(x)) represent?

• The sum of f(x) and g(x)

• The product of f(x) and g(x)

• g(x) evaluated at f(x)

• f(x) evaluated at g(x)

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

• (x - 2)^2

• x^2 - 4x + 4

• x^2 - 2

• x^2 + 4x - 4

What happens to the domain when composing functions f(x) and g(x)?

• It remains the same

• It includes restrictions from both functions

• It only includes restrictions from g(x)

• It only includes restrictions from f(x)

How can compositions be evaluated using tables?

• By adding values

• By dividing values

• By multiplying values

• By substituting values