Understanding Inverses: Logs and Exponentials

The video tutorial explains how to find the inverse of functions, focusing on logarithmic and exponential functions. It begins with an introduction to inverse functions, detailing the steps to replace function notation, switch variables, and solve for the desired variable. The tutorial then demonstrates finding the inverse of a logarithmic function by switching x and y, isolating the logarithm, and converting it to exponential form. Finally, it covers finding the inverse of an exponential function by isolating the base and rewriting it as a logarithm.

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

• Set the function notation

• Solve for y

• Switch x and y in the equation

• Isolate the logarithm

When finding the inverse of a logarithmic function, what do you do after switching x and y?

• Add a constant to both sides

• Isolate the logarithm

• Multiply by the base

• Divide by the coefficient

What is the inverse of a logarithmic function?

• Another logarithmic function

• An exponential function

• A polynomial function

• A trigonometric function

What is the expected result when starting with an exponential function?

• Another exponential function

• A trigonometric function

• A logarithmic function

• A polynomial function

In the process of finding the inverse of an exponential function, what is the first step?

• Divide by the coefficient

• Multiply by the base

• Switch x and y

• Add a constant to both sides

How do you isolate the base in an exponential function?

• Add a constant to both sides

• Multiply by the base

• Switch x and y

• Divide by the coefficient

What is the final step in rewriting an exponential function as a logarithm?

• Switch x and y

• Multiply by the base

• Rewrite it as a log

• Add a constant to both sides

What is the base of the logarithm when rewriting an exponential function?

• The coefficient of the function

• The constant added to the function

• The exponent of the function

• The base of the exponential function

What do you do to get the y out of the exponent in an exponential function?

• Switch x and y

• Rewrite it as a log

• Multiply by the base

• Add a constant to both sides

What indicates that a function is an inverse?

• A constant term

• A positive exponent

• A negative exponent

• A coefficient of one