Finding Inverses of Exponential Functions

The video tutorial explains how to find the inverse of a function, specifically f(x) = e^(2x) + 3. It outlines four main steps: replacing the function with a variable, interchanging variables, solving for y, and using proper notation to express the inverse function. The tutorial emphasizes the importance of each step and provides a detailed walkthrough of the process, including the use of natural logarithms to isolate y.

What is the initial function given in the problem?

• f(x) = ln(x) + 3

• f(x) = e^(2x) + 3

• f(x) = e^(x) + 2

• f(x) = 2x + 3

What is the first step in finding the inverse of a function?

• Solve for 'y'

• Replace the function with a new variable

• Use proper notation

• Interchange the variables

In the process of finding the inverse, what do you replace 'y' with?

• z

• x

• a

• b

What mathematical operation is used to bring down the exponent in the third step?

• Addition

• Multiplication

• Subtraction

• Natural logarithm

What is the formula used when taking the natural log of e to the power of x?

• ln(e^x) = 1

• ln(e^x) = e

• ln(e^x) = 0

• ln(e^x) = x

After taking the natural log, what is the next step to isolate 'y'?

• Divide both sides by 2

• Multiply both sides by 2

• Subtract 3 from both sides

• Add 3 to both sides

What is the final expression for 'y' after solving the equation?

• y = ln(x) - 3 / 2

• y = ln(x) + 3 / 2

• y = ln(x - 3) / 2

• y = ln(x + 3) / 2

What is the proper notation for the inverse function?

• F(x)

• F inverse of x

• G(x)

• H(x)

What is the inverse function of f(x) = e^(2x) + 3?

• F inverse of x = ln(x + 3) / 2

• F inverse of x = ln(x - 3) / 2

• F inverse of x = ln(x) / 2

• F inverse of x = ln(x) + 3 / 2

What is the purpose of using proper notation in the final step?

• To confuse the reader

• To make the function look complex

• To ensure clarity and correctness

• To simplify the function