Composite Functions and Their Evaluations

The video tutorial explains composite functions, which are created when one function is used as the input for another. It covers different notations for composite functions and emphasizes the difference between composition and multiplication of functions. The tutorial provides step-by-step examples of finding F of G of X and G of F of X, including simplifying expressions and evaluating these functions at specific values. The video aims to help viewers understand and apply the concept of composite functions in mathematics.

What is a composite function?

• A function that divides two functions

• A function that uses another function as its input

• A function that adds two functions

• A function that multiplies two functions

How can composite functions be written?

• F(x) - G(x)

• F(x) / G(x)

• F(x) + G(x)

• F(G(x)) or F ∘ G(x)

What is the interior function in F(G(x))?

• None of the above

• G(x)

• H(x)

• F(x)

What does it mean to substitute G(x) into F(x)?

• Multiply G(x) by F(x)

• Add G(x) to F(x)

• Replace every x in F(x) with G(x)

• Divide F(x) by G(x)

What is the result of simplifying 2(x + 6) + 5?

• 2x + 17

• 2x + 12

• 2x + 5

• 2x + 11

In G(F(x)), what is the role of F(x)?

• It is not used

• It is the result of the function

• It is the interior function

• It is the exterior function

What is the final result of G(F(x)) when F(x) = 2x + 5?

• 2x + 5

• 2x + 6

• 2x + 17

• 2x + 11

What is the first step in finding F(G(x)) when G(x) = x - 1?

• Multiply x by 2

• Square x

• Add 1 to x

• Replace x in F(x) with x - 1

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

• x^2 + 2x + 5

• x^2 + 2x + 6

• x^2 - 2x + 5

• x^2 - 2x + 6

In G(F(x)), what do you do with F(x)?

• Add it to G(x)

• Replace x in G(x) with F(x)

• Multiply it by G(x)

• Subtract it from G(x)