   Inverse Functions f ^-1 (y) and the Logarithm x = ln y
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Video Lecture 11 of 18
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### Lecture Description

In this video lecture, Prof. Gilbert Strang discusses Inverse Functions f ^-1 (y) and the Logarithm x = ln y.

For the usual y = f(x), the input is x and the output is y. For the inverse function x = f^-1(y), the input is y and the output is x. If y equals x cubed, then x is the cube root of y: that is the inverse. If y is the great function e^x, then x is the natural logarithm ln y. Start at y, go to x = ln y, then back to y = e^(ln y). So the logarithm is the exponent that produces y. The logarithm of y = e^5 is ln y = 5. Logarithms grow very slowly.

### Course Description

Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject.

The series is divided into three sections:
Introduction
- Why Professor Strang created these videos
- How to use the materials

Highlights of Calculus
- Five videos reviewing the key topics and ideas of calculus
- Applications to real-life situations and problems
- Additional summary slides and practice problems

Derivatives
- Twelve videos focused on differential calculus
- More applications to real-life situations and problems
- Additional summary slides and practice problems

Acknowledgements
Special thanks to Professor J.C. Nave for his help and advice on the development and recording of this program.The video editing was funded by the Lord Foundation of Massachusetts.