Understanding Function Operations

The video tutorial explains how to add two functions, f(x) and g(x), and introduces the notation f+g(x). It starts by defining the functions f(x) = 9 - x^2 and g(x) = 5x^2 + 2x + 1. The tutorial then clarifies that f+g(x) is shorthand for f(x) + g(x). The process of adding these functions is demonstrated, resulting in a new function: 4x^2 + 2x + 10. The video emphasizes understanding the notation and the steps involved in combining functions.

What is the correct expression for f(x) as given in the video?

• x + 9

• x^2 - 9

• 9 - x^2

• 9 - x

What does the notation f + g(x) represent?

• The division of f(x) by g(x)

• The difference between f(x) and g(x)

• The sum of f(x) and g(x)

• The product of f(x) and g(x)

How is the new function f + g(x) created?

• By dividing f(x) by g(x)

• By adding f(x) and g(x)

• By subtracting g(x) from f(x)

• By multiplying f(x) and g(x)

What is the expression for g(x) as given in the video?

• 2x^2 + 5x + 1

• 5x^2 + 2x + 1

• 5x + 2x^2 + 1

• x^2 + 5x + 2

What is the first step in simplifying the expression for f + g(x)?

• Combine the x terms

• Remove the parentheses

• Factor the expression

• Combine the constant terms

What is the result of combining the x^2 terms in f + g(x)?

• 6x^2

• 4x^2

• 5x^2

• 3x^2

What is the final expression for f + g(x)?

• 5x^2 + 3x + 9

• 5x^2 + 2x + 9

• 4x^2 + 3x + 10

• 4x^2 + 2x + 10

What does the final expression for f + g(x) represent?

• A new function created by multiplying f(x) and g(x)

• A new function created by adding f(x) and g(x)

• A new function created by subtracting g(x) from f(x)

• A new function created by dividing f(x) by g(x)

What is the sum of the constant terms in f + g(x)?

• 8

• 9

• 10

• 11

How many first-degree terms are there in the final expression for f + g(x)?

• One

• None

• Two

• Three