The video tutorial explains how to determine if two functions are inverses by verifying that the composite functions F(G(x)) and G(F(x)) both equal x. It provides two examples: the first with F(x) = 4x and G(x) = x/4, which are inverses, and the second with F(x) = 2x + 9 and G(x) = x/2 - 9, which are not inverses. The tutorial emphasizes the importance of verifying both composite functions to confirm inverse relationships.

What is the primary purpose of inverse functions?

• To divide inputs by a constant

• To add a constant to inputs

• To multiply inputs by a constant

• To undo the effect of another function

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

In the first example, what operation does F(x) perform?

• Subtracts 4

• Adds 4

• Multiplies by 4

• Divides by 4

Tags

CCSS.HSF-BF.B.4B

What must be true for two functions to be considered inverses?

• F(x) = G(x)

• F(x) + G(x) = 0

• F(G(x)) = G(F(x))

• F(G(x)) = x and G(F(x)) = x

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

In the second example, what is the expression for G(x)?

• x divided by 2 minus 9

• 2x minus 9

• 2x plus 9

• x divided by 2 plus 9

Tags

CCSS.HSF-BF.A.1C

What is the result of F(G(x)) in the second example?

• x - 9

• x + 9

• 2x

• x

Tags

CCSS.HSF-BF.B.4B

Why are F(x) = 2x + 9 and G(x) = x/2 - 9 not inverses?

• G(F(x)) equals x

• F(G(x)) does not equal x

• They are inverses

• Both F(G(x)) and G(F(x)) equal x

Tags

CCSS.HSF-BF.A.1C

What is the simplified form of G(F(x)) in the second example?

• 2x

• x

• x - 9

• x + 9

Tags

CCSS.HSF-BF.B.4B

What is the key takeaway from verifying inverse functions?

• Neither composite function should equal x

• Both composite functions must equal x

• Only F(G(x)) needs to equal x

• Only one composite function needs to equal x

Tags

CCSS.HSF-BF.B.4B

What happens if one composite function does not equal x?

• The functions are undefined

• The functions are not inverses

• The functions are inverses

• The functions are equal

Tags

CCSS.HSF-BF.B.4B

What is the final conclusion about the functions in the second example?

• They are inverses

• They are undefined

• They are not inverses

• They are equal

Tags

CCSS.HSF-BF.B.4B