Evaluating Composite Functions: Concepts and Examples

This video tutorial introduces composite functions, explaining them as a combination of two or more functions where the output of one function becomes the input of another. The instructor uses simple examples to illustrate the concept, emphasizing the importance of understanding composite functions for calculus. The video also covers the order of operations in composite functions and provides practice problems to reinforce learning. The tutorial concludes by highlighting the significance of composite functions in understanding inverse functions and logarithms.

What is a composite function?

• A function that only takes one input.

• A function that is always linear.

• A function that cannot be graphed.

• A function that is composed of two or more functions.

Why do we use different names for functions in composite functions?

• To ensure the function is linear.

• To simplify the function.

• To make the function more complex.

• To avoid confusion.

If G(x) = 2x and F(x) = x^2, what is F(G(2))?

• 4

• 16

• 8

• 32

What is the first step in evaluating a composite function?

• Evaluate the outermost function.

• Simplify the function.

• Evaluate the innermost function.

• Graph the function.

How do you write the composite function of F and G?

• F + G

• F(G(x))

• G(F(x))

• G - F

If F(x) = 3x - 5 and G(x) = √x, what is F(G(4))?

• 1

• 2

• 3

• 4

What is the result of G(F(4)) if F(x) = 3x - 5 and G(x) = √x?

• 7

• √7

• 2

• 1

In general, is F(G(x)) equal to G(F(x))?

• Yes, but only for linear functions.

• No, except for inverse functions.

• No, never.

• Yes, always.

What is the composite function F(G(x)) if F(x) = 3x - 5 and G(x) = √x?

• 3√x - 5

• √(3x - 5)

• 3x - 5

• √x

What is the composite function G(F(x)) if F(x) = 3x - 5 and G(x) = √x?

• √x

• 3x - 5

• √(3x - 5)

• 3√x - 5