Finding Inverse Functions with Logarithms

The video tutorial explains how to find the inverse of the function 3^(x-1) + 2. It involves replacing f(x) with y, switching x and y, solving for y, and using logarithms to simplify the equation. The final inverse function is expressed in terms of log base 3. The tutorial provides a step-by-step approach to understanding and solving the problem.

What is the initial function we are trying to find the inverse of?

• x to the 3 minus 1 plus 2

• 3 to the x minus 1 plus 2

• 3 to the x plus 1 minus 2

• 3 to the x minus 2 plus 1

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

• Switch x and y

• Replace f(x) with y

• Add 2 to both sides

• Take the log of both sides

What is the purpose of replacing f(x) with y in the process?

• To prepare for switching x and y

• To solve for x

• To simplify the equation

• To take the logarithm

After replacing f(x) with y, what is the next step?

• Switch x and y

• Add 1 to both sides

• Subtract 2 from both sides

• Take the log base 3

Why do we switch x and y in the process of finding an inverse?

• To express the inverse function

• To change the base of the logarithm

• To solve for y

• To isolate the term

What operation is performed to isolate the term 3 to the y minus 1?

• Add 2 to both sides

• Multiply both sides by 3

• Subtract 2 from both sides

• Divide both sides by 3

What is the significance of subtracting 2 from both sides?

• To express the inverse function

• To solve for x

• To isolate the exponential term

• To change the base of the logarithm

Which logarithmic property is used to simplify the equation?

• log base b of x equals x to the b

• log base x of b equals b to the x

• log base b of x equals b to the x

• log base b of b to the x equals x

What does the property log base b of b to the x equals x help us achieve?

• It simplifies the equation

• It helps in isolating y

• It changes the base of the logarithm

• It solves for x

What is the base used in the logarithm for this problem?

• Base 2

• Base e

• Base 3

• Base 10