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

Tags

CCSS.HSF.IF.A.2

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

Tags

CCSS.HSF-BF.A.1B

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

Tags

CCSS.HSF-BF.A.1B

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

Tags

CCSS.HSA.APR.A.1

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

Tags

CCSS.HSF-BF.A.1B

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

Tags

CCSS.HSF-BF.A.1C

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

Tags

CCSS.HSF-BF.A.1C

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

Tags

CCSS.HSF-BF.A.1C

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

• 4X + 1

• 4X + 2

• 4X + 3

• 4X + 4

Tags

CCSS.HSF-BF.A.1C

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

Tags

CCSS.HSF-BF.A.1C