EDB — 1VH

Exercises

1. [1VH]

   • Show that there is an unique continuous function\(f:(-1,1)→ℝ\) that satisfies

     \[ f(x) = x \cos (f(x))~ ~ . \]

   • Fixed \(a,b\), show that there exist a finite number of continuous \(f:(-a,b)→ℝ\) satisfying

     \[ f(x) = x \cos (f(x))~ ~ ∀ x∈(a,b). \]
   Solution 1

   [1VJ]↺↻