Function Composition and Evaluation

The video tutorial covers evaluating composite functions, specifically g(f(3)) and g(f(f(3))), using given functions and values. It demonstrates how to use a table to find g(f(-2)) and explains deriving an expression for f(g(x)) by substituting one function into another. The tutorial emphasizes understanding composite functions and their evaluations through examples and step-by-step calculations.

What is the first step in evaluating g(f(3)) given f(x) = x^2 + 3x - 8?

• Find the value of g(3)

• Calculate f(3)

• Directly substitute into g

• Solve for x in f(x)

What is the value of f(3) if f(x) = x^2 + 3x - 8?

• 1

• 6

• 10

• 9

How do you find g(f(f(3))) if f(3) = -7 and f(-7) = -4?

• Use f(3) directly

• Find f(-4)

• Evaluate g(-4)

• Calculate g(-7)

What is the value of g(f(f(3))) given f(3) = -7, f(-7) = -4, and g(-4) = 5?

• 7

• 5

• 6

• 4

What is the first step in using a table to find g(f(-2))?

• Directly find g(f(-2))

• Look up g(-2)

• Calculate g(4)

• Find f(-2)

If f(-2) = 4, what is g(f(-2)) using the table?

• 6

• 5

• 8

• 7

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

• x^2 + 2x - 3

• 4x^2 - 12x + 14

• 2x^2 - 3x + 5

• (2x - 3)^2 + 5

What is the result of multiplying (2x - 3) by itself?

• 4x^2 + 9

• 2x^2 - 6x + 9

• 4x^2 - 12x + 9

• 4x^2 - 9

What is the final step in simplifying f(g(x)) for f(x) = x^2 + 5 and g(x) = 2x - 3?

• Add 5 to the result

• Multiply by 2

• Subtract 3

• Divide by x

Which of the following is the correct expression for f(g(x))?

• 4x^2 + 5

• x^2 + 4x - 3

• 2x^2 - 3x + 5

• 4x^2 - 12x + 14