Inverse Functions and Their Applications

The video tutorial explains how to determine inverse function values without explicitly finding the inverse function. It begins by discussing the concept of inverse functions and how they reverse the operations of the original function. The tutorial then provides examples using specific functions, demonstrating how to find inputs that yield desired outputs, thereby determining inverse values. The video concludes with a second example using a linear function, reinforcing the method and understanding of inverse functions.

What is the main purpose of an inverse function?

• To square the input of the original function

• To reverse the operation of the original function

• To double the output of the original function

• To halve the input of the original function

In the first example, what was the output of F when the input was 9?

• 3

• 4

• 5

• 6

What is the inverse function value of 4 for function F?

• 25

• 16

• 4

• 9

Which input for function F resulted in an output of 6?

• 16

• 9

• 4

• 25

What is the inverse function value of 6 for function F?

• 16

• 25

• 9

• 4

In the second example, what is the formula for function G?

• G(x) = 2x - 1

• G(x) = x/2 - 1

• G(x) = x^2 + 1

• G(x) = 2x + 1

What input for function G gives an output of 3?

• 3

• 2

• 1

• 4

What is the inverse function value of 3 for function G?

• 4

• 3

• 2

• 1

What input for function G gives an output of 7?

• 5

• 2

• 3

• 4

What is the inverse function value of 7 for function G?

• 3

• 2

• 4

• 5