Exploring Function Operations in Algebra 2

This video tutorial covers function operations, including addition, subtraction, multiplication, division, and composition of functions. It explains how to find the domain of resulting functions and provides examples for each operation. The tutorial also discusses the importance of factoring in division and the process of composing functions with examples.

What is the result of adding the functions f(x) = 3x + 4 and g(x) = x² - 5x + 2?

• x² + 2x + 6

• x² - 8x + 6

• x² - 2x + 6

• x² + 8x + 6

When subtracting the function g(x) from f(x), what is the correct result?

• x² - 8x - 2

• x² + 8x + 2

• -x² - 8x + 2

• -x² + 8x + 2

If the demand function is d(x) = 5000 - 10x and the price function is p(x) = x, what is the revenue function?

• 5000 - 10x

• 5000x + 10x²

• 5000x - x²

• 5000x - 10x²

What is the result of dividing f(x) = x - 7 by g(x) = 2x² - 13x - 7 after factoring?

• 1 / (x - 7)

• x / (x - 7)

• x / (2x + 1)

• 1 / (2x + 1)

What are the domain restrictions when dividing f(x) by g(x)?

• x cannot be -7 and x cannot be -1/2

• x cannot be -7 and x cannot be 1/2

• x cannot be 7 and x cannot be 1/2

• x cannot be 7 and x cannot be -1/2

What is the result of the composition f(g(3)) if f(x) = x² and g(x) = x + 1?

• 4

• 9

• 1

• 16

What is the general form of f(g(x)) if f(x) = x² and g(x) = x + 1?

• x² + x + 1

• x² - x + 1

• x² + 2x + 1

• x² - 2x + 1

What is the first step in finding f(g(x)) for f(x) = x² and g(x) = x + 1?

• Square x

• Add x and 1

• Substitute x + 1 into f(x)

• Multiply x and 1

What is the simplified form of f(g(x)) if f(x) = √(x + 7) and g(x) = 2x - 5?

• √(2x - 2)

• √(2x + 12)

• √(2x + 2)

• √(2x - 12)

What is the result of f(g(x)) if f(x) = x² + x + 2 and g(x) = 4 - x?

• x² + 9x - 22

• x² - 9x - 22

• x² + 9x + 22

• x² - 9x + 22