Homework 9

Details

1. (8) Let \(f:\mathbb{R}\rightarrow\mathbb{R}\) be defined by \(f(x)=x^3-1\).
   1. Prove that \(f\) is one-to-one.
   2. Prove that \(f\) is onto.
   3. Prove that \(f\) is invertible.
   4. Find \(f^{-1}(x)\).
2. (8) AIDM Problem 3.24 (Page 131).
   You have to prove 3 things! One of them is so easy it can seem confusing. The other two are not that difficult. Look at the examples in the book for inspiration.