Evaluating the Composition of Two Functions

The video tutorial covers the composition of two functions and their evaluation. It begins with an introduction to function composition and evaluation, followed by a simple example of evaluating a function. The tutorial then delves into the composition of functions, explaining how to simplify and evaluate them. Examples are provided to illustrate the process of evaluating composed functions, including the use of square roots and simplification techniques.

What is the result of evaluating the function F(x) = x + 3 at x = 2?

• 4

• 5

• 7

• 6

In the composition G(F(x)), if F(x) = sqrt(x) + 4, what is the expression for G(F(x))?

• (sqrt(x) + 4)^2 - 1 / 3

• (sqrt(x) + 4)^2 - 1

• sqrt(x) + 4

• x^2 + 4

What is the simplified form of G(x) if G(x) = (x + 3) / 3?

• x / 3

• x + 3

• x / 3 + 1

• x + 1

How do you find G(5) if G(x) = (x^2 - 1) / 3?

• Plug 5 into x in G(x)

• Multiply 5 by G(x)

• Subtract 5 from G(x)

• Add 5 to G(x)

What is the value of G(5) when G(x) = (x^2 - 1) / 3?

• 11

• 10

• 9

• 8

What is the result of F(G(5)) if F(x) = sqrt(x) + 4 and G(5) = 8?

• 2 * sqrt(3)

• sqrt(12)

• 4 * sqrt(2)

• sqrt(8) + 4

Which method can be used to evaluate F(G(5))?

• Algebraic manipulation

• Graphical method

• Direct substitution

• Numerical approximation