Key Concepts
- If g(x) is the inverse of f(x), then
- g(f(x))=f(g(x))=x.
- 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 y=f(x) for x as a function of y. Then exchange the labels x and y.
- The graph of an inverse function is the reflection of the graph of the original function across the line y=x.
Glossary
- inverse function
- for any one-to-one function f(x), the inverse is a function f−1(x) such that f−1(f(x))=x for all x in the domain of f; this also implies that f(f−1(x))=x for all x in the domain of f−1
Candela Citations
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- Precalculus. Authored by: Jay Abramson, et al.. Provided by: OpenStax. Located at: http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175. License: CC BY: Attribution. License Terms: Download For Free at : http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.