Algebraic Demonstration of an Odd Function
Prove algebraically that the function \(f(x) = \frac{2x}{1-x^2}\) is odd by showing that \(f(-x) = -f(x)\).
Contrapositive Approach to Domain/Range Proof
Let \(f: A \rightarrow B\) be a function such that if \(x \in A\) then \(f(x) \in B\). Prove that if \(f(x) \notin B\), then \(x \notin A\) using a contrapositive argument.