Inverse Functions and Operations

The video tutorial explains how to write inverse functions by understanding the order of operations. It emphasizes using a two-way table to avoid mistakes. The instructor provides three examples, demonstrating how to reverse operations to find the inverse function. Each example involves different operations, and the final example includes simplification.

What is the primary purpose of an inverse function?

• To add a constant to the original function

• To undo the operation of the original function

• To perform the same operation as the original function

• To multiply the original function by a constant

Why is it important to know the order of operations when dealing with inverse functions?

• To ensure the function is continuous

• To avoid making mistakes in calculations

• To simplify the function

• To make the function more complex

What is the first step in using a two-way table to find an inverse function?

• Start with the original function

• Start with the variable z

• Start with the variable y

• Start with the inverse function

In the first example, what is the first operation performed on x?

• Adding 6

• Dividing by -3

• Multiplying by -3

• Subtracting 6

What is the inverse operation of adding 6?

• Dividing by 6

• Adding 3

• Multiplying by 6

• Subtracting 6

In the second example, what is the last operation performed on x?

• Dividing by 15

• Subtracting 7

• Multiplying by 10

• Adding 7

What is the inverse operation of dividing by 15?

• Adding 15

• Multiplying by 15

• Subtracting 15

• Dividing by 10

In the third example, what is the first operation performed on x?

• Subtracting 5

• Adding 5

• Dividing by 4

• Multiplying by 2

What is the inverse operation of subtracting 5?

• Multiplying by 5

• Subtracting 2

• Dividing by 5

• Adding 5

How can the final inverse function in the third example be simplified?

• By multiplying the numerator by 2

• By dividing 4 by 2

• By adding 4 to the numerator

• By subtracting 2 from the numerator