Understanding Inverse Functions

The video tutorial explains the concept of inverse functions, emphasizing that two functions are inverses if their compositions result in the original input. It details the process of verifying inverse functions by checking both compositions: f(g(x)) = x and g(f(x)) = x. The tutorial includes a step-by-step example to demonstrate this verification process, ensuring that the output matches the input in both cases.

What is the basic idea behind two functions being inverses?

• They are identical.

• They undo each other.

• They add up to zero.

• They multiply to give a constant.

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What does the composition of two inverse functions result in?

• A different function.

• The original input.

• Zero.

• A constant value.

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CCSS.HSF-BF.B.4B

How do you verify if two functions are inverses?

• By checking if their sum is zero.

• By checking if their product is one.

• By checking if they are equal.

• By checking if their compositions result in the original input.

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CCSS.HSF-BF.A.1C

What is the first step in verifying f(g(x))?

• Subtracting the functions.

• Plugging g(x) into f.

• Dividing the functions.

• Multiplying the functions.

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CCSS.HSF-BF.A.1C

What is the result of the composition f(g(x)) in the example?

• 2x

• x + 1

• x

• 0

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CCSS.HSF-BF.A.1C

What happens to the terms in f(g(x)) when simplified?

• They cancel out to give zero.

• They add up to a constant.

• They simplify to x.

• They remain unchanged.

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CCSS.HSF-BF.A.1C

What is the first step in verifying g(f(x))?

• Multiplying the functions.

• Plugging f(x) into g.

• Subtracting the functions.

• Dividing the functions.

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CCSS.HSF-BF.A.1C

What is the result of the composition g(f(x)) in the example?

• 0

• x

• x + 1

• 2x

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CCSS.HSF-BF.A.1C

Why is it important to check both f(g(x)) and g(f(x))?

• To find the sum of the functions.

• To ensure they are equal.

• To determine the product of the functions.

• To verify they both result in the original input.

What is the significance of the invisible 1 in the calculations?

• It adds a constant.

• It is irrelevant.

• It helps in distributing terms.

• It changes the function.