Understanding Function Composition

What symbol is used to denote the composition of two functions?

• A square

• A circle

• A plus symbol

• A multiplication symbol

What does the notation f(g(x)) imply?

• Multiplying f(x) by g(x)

• Adding f(x) to g(x)

• Substituting g(x) into f(x)

• Dividing f(x) by g(x)

What does the composition of functions involve?

• Substituting one function into another

• Finding the derivative of two functions

• Adding two functions together

• Multiplying two functions together

What is the correct interpretation of the notation 'F Circle G'?

• F divided by G

• F composed with G

• F multiplied by G

• F added to G

If f(x) = x^2 + x and g(x) = 4 - x, what is f(g(x))?

• x^2 - 9x + 20

• 4x^2 - x + 4

• x^2 - 8x + 16

• x^2 - 9x + 16

How do you find f(g(x)) given f(x) and g(x)?

• By dividing f(x) by g(x)

• By adding f(x) to g(x)

• By substituting g(x) into f(x)

• By multiplying f(x) and g(x)

If f(x) = x^2 + x and g(x) = 4 - x, what is g(f(x))?

• -x^2 - x + 4

• -x^2 + x + 4

• x^2 + 5x + 4

• 4 - x^2 - x

Does the order of composition (f(g(x)) vs g(f(x))) always yield the same result?

• No, it varies

• Only if one of the functions is constant

• Yes, always

• Only for linear functions

If the composition of two functions is commutative, what does it imply?

• It implies nothing about the functions

• f(g(x)) = g(f(x)) for all x

• f(g(x)) * g(f(x)) = 1

• f(g(x)) + g(f(x)) = 0

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

• -8

• -9

• 9

• 8