Exploring Composition Functions

What is the first step in solving a function given a value of x?

• Divide the value by the function

• Multiply the value by the function

• Substitute the value into the function

• Add the value to the function

In the warm-up problem, what is the simplified form of the expression 5 - 3(2b + 1)?

• 5 + 6b

• 5 - 6b

• 2 - 6b

• 2 + 6b

What is a composite function?

• A function that divides two functions

• A function that adds two functions

• A function that multiplies two functions

• A function that is substituted into another function

How is the notation f(g(x)) pronounced?

• f of g times x

• f of g plus x

• f of g divided by x

• f of g of x

In the example, what is the simplified form of g(f(x)) if f(x) = 2x^2 + 3 and g(x) = 5 - x?

• 5 - 2x^2 - 3

• 2 - 2x^2

• 5 - 2x^2 + 3

• 2x^2 + 3 - 5

What is the correct order of operations when simplifying a composite function?

• Exponents, Parentheses, Multiplication, Division, Addition, Subtraction

• Addition, Subtraction, Multiplication, Division

• Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

• Multiplication, Division, Addition, Subtraction

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

• 2(5 - x)^2 + 3

• 2x^2 + 3 - x

• 5 - 2x^2 + 3

• 2(5 - x) + 3

In the complex example, what is the first step in simplifying the composition function g(f(x + 1))?

• Substitute x + 1 into f

• Simplify f first

• Substitute f into g

• Simplify g first

What is the simplified form of 5 - (2(x + 1)^2 + 3)?

• 2x^2 + 4x + 3

• 2x^2 + 4x + 5

• 5 - 2x^2 - 4x - 5

• 5 - 2x^2 - 4x - 3

What is the final simplified form of the expression 2(5 - x)^2 + 3?

• 2x^2 - 20x + 53

• 2x^2 + 20x + 53

• 2x^2 - 20x + 50

• 2x^2 + 20x + 50