Let us say that a function is \(\textbf{mathian}\) if it has a certain property we’ve discovered that’s hard to prove directly. However, after much work we have proved two important facts about \(\textbf{mathian}\) functions.
1. If \(f(x)\) is \(\textbf{mathian}\) then so is \(-f(x)\). For instance, if \(f_1(x)=x^2\) were \(\textbf{mathian}\), then \(f_2(x)=-x^2\) would be too.
2. If \(f(x)\) and \(g(x)\) are \(\textbf{mathian}\), then so is max(\(f(x)\), \(g(x)\)). (Recall that max equals the larger of two values; or equals the common value if they are the same.)
(a) Prove that if \(f(x)\) is \(\textbf{mathian}\), then so is \(|f(x)|\). Hint: express \(|f(x)|\) using \(f\), \(-f\) and max.
(b) Prove that if \(f(x)\) and \(g(x)\) are \(\textbf{mathian}\), then so is min(\(f(x)\), \(g(x)\)).
Please help!!! Thank you!!!
