Mathematics (AS)·Graphs and functions · NSSCAS 1.3.3
One-one & inverse functions
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Some functions can be undone — and in this lesson you will learn exactly which ones, and how. You will test whether a function is one-one using the horizontal line test, rescue a many-one function by restricting its domain, and find inverses with a calm three-step method that works every time. You will also sketch a function and its inverse as perfect mirror images in the line y = x. By the end, questions like 'find f inverse and state its domain' will feel like free marks.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.3.3):
- Interpret the terms one-one function and inverse function
- Determine whether or not a given function is one-one, using the horizontal line test and restricting a domain to make a function one-one
- Find the inverse of a one-one function in simple cases
- Sketch graphs of a function and its inverse for a specified domain, as reflections in the line y = x
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