Exploring Operations with Functions and Compositions

Professor Dave explains how to work with functions, starting with basic evaluation and moving to more complex operations like algebraic substitution, function operations (addition, subtraction, multiplication, division), and composite functions. The video also covers advanced manipulations and checks comprehension of these concepts.

If F of X equals 2X + 1, what is F of X + 3?

• 2X + 5

• 2X + 6

• 2X + 7

• 2X + 4

Given F of X = 2X + 1 and G of X = X - 5, what is F + G of X?

• 2X - 5

• 3X - 4

• 3X - 5

• 2X - 4

What is the result of F minus G of X if F of X = 2X + 1 and G of X = X - 5?

• X - 6

• X + 6

• X + 4

• X - 4

What is the product of F of X and G of X if F of X = 2X + 1 and G of X = X - 5?

• 2X^2 - 9X - 5

• 2X^2 - 9X + 5

• 2X^2 - 10X - 5

• 2X^2 - 10X + 5

What is the domain of F over G of X if F of X = 2X + 1 and G of X = X - 5?

• All real numbers except -5

• All real numbers except 5

• All real numbers except 0

• All real numbers

How do we denote the composite function F of G of X?

• F * G of X

• F + G of X

• F(G(X))

• F - G of X

If F of X = 2X + 1 and G of X = X - 5, what is F of G of X?

• 2X - 10

• 2X - 9

• 2X - 4

• 2X - 5

What is G of F of X if F of X = 2X + 1 and G of X = X - 5?

• 2X - 4

• 2X - 10

• 2X - 9

• 2X - 5

What is F of F of X if F of X = 2X + 1?

• 4X + 1

• 4X + 2

• 4X + 3

• 4X + 4

Which of the following is not the same as squaring the function?

• F of F of F of X

• F of F of X

• F squared of X

• G of G of X