Key Concepts & Glossary
Key Concepts
- If is the inverse of , then
- .
- Each of the toolkit functions has an inverse.
- For a function to have an inverse, it must be one-to-one (pass the horizontal line test).
- A function that is not one-to-one over its entire domain may be one-to-one on part of its domain.
- For a tabular function, exchange the input and output rows to obtain the inverse.
- The inverse of a function can be determined at specific points on its graph.
- To find the inverse of a formula, solve the equation for as a function of . Then exchange the labels and .
- The graph of an inverse function is the reflection of the graph of the original function across the line .
Glossary
- inverse function
- for any one-to-one function , the inverse is a function such that for all in the domain of ; this also implies that for all in the domain of