Finding Inverse Functions Steps

The video tutorial explains how to find the inverse of a function where f(x) equals e^x over (e^x + 2). It begins by replacing f(x) with y, interchanging x and y, and then solving for y. The process involves manipulating the equation, factoring, and using logarithms to isolate y. The final step is to express the inverse function in a simplified form.

What is the initial function f(x) that we are trying to find the inverse of?

• f(x) = e^x + 2

• f(x) = 2e^x / (e^x + 1)

• f(x) = e^x / (e^x + 2)

• f(x) = e^x - 2

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

• Use logarithms

• Solve for y

• Interchange x and y

• Replace f(x) with y

After interchanging x and y, what is the new equation?

• x = e^y + 2

• x = e^y / (e^y + 2)

• x = 2e^y / (e^y + 1)

• x = e^y - 2

What is the key step in solving for y in the equation x = e^y / (e^y + 2)?

• Dividing both sides by x

• Subtracting e^y from both sides

• Multiplying both sides by e^y + 2

• Adding 2 to both sides

What operation is used to bring down the variable from the exponent?

• Addition

• Subtraction

• Multiplication

• Logarithm

What is the expression for y after applying the logarithm?

• y = ln(x - 1)

• y = ln(x)

• y = ln(2x)

• y = ln(-2x / (x - 1))

What is the final step in finding the inverse function?

• Replace x with f inverse of y

• Replace y with f(x)

• Replace y with f inverse of x

• Replace x with y

How can the expression for the inverse function be simplified?

• By adding 1 to both the numerator and denominator

• By factoring a negative out of the top

• By subtracting 1 from both the numerator and denominator

• By factoring a positive out of the top

What is the simplified form of the inverse function?

• ln(-2x / (1 - x))

• ln(2x / (1 - x))

• ln(-2x / (x + 1))

• ln(2x / (x - 1))

Which of the following is a valid form of the inverse function?

• ln(x / (x - 2))

• ln(-x / (2 - x))

• ln(2x / (1 - x))

• ln(-2x / (x - 1))