Find inverse functions for simple invertible functions, including rational examples.
Decide one-to-one status from fixed evidence
Problem
A function is strictly increasing on its entire domain. Use that evidence to determine its one-to-one status, horizontal-line-test result, and whether its inverse relation is a function.
Use the graph's strictly increasing behavior to think about repeated outputs and the horizontal-line test.Open full size
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What this problem is really about
One-to-one behavior is about whether an output can repeat, not merely whether the original relation passes the vertical-line test. Translate strict increase into an ordering statement for two inputs; that ordering determines whether their outputs can coincide. The same conclusion can then be expressed graphically with horizontal lines and transferred to the inverse relation by swapping coordinates.
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