E-RI02 · An inverse on a finite increasing branch
Let \(f(x)=9-(2x+1)^2\), \(\displaystyle - 2\le x< - \frac{1}{2}\).
Explain why \(f\) is one-one on this domain and find its range.
Find \(f^{-1}\), with its domain and range.
Find all real \(k\) for which \(\displaystyle f^{- 1}(k)\ge - \frac{3}{2}\).
Complete-answer checking, worked solutions and indicative written criteria.
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