The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Inverse functions, domain and range
Distinguish a function from a one-one function.
Find ranges, respecting unattained and excluded values.
Find and verify inverse rules with their domains and ranges.
A function gives exactly one output for each allowed input. One-one means distinct inputs give distinct outputs. For an inverse, solve \(y=f(x)\) for \(x\), then exchange variable names. Domain and range swap; \(f^{-1}\) does not mean \(\displaystyle \frac{1}{f}\).