Understanding Inverse Functions and Their Properties

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

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

• Subtracts 4

• Adds 4

• Multiplies by 4

• Divides by 4

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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

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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

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

• x - 9

• x + 9

• 2x

• x

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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

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

• 2x

• x

• x - 9

• x + 9

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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

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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

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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

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