Algebra · Functional equations · Substitution · Image of a map · Quadratic equations · Am gm
Problem 1, 2009
How many functions \(f \colon \mathbb{R}^{+} \to \mathbb{R}\) are there such that
\[ f\left(x + \frac{1}{x}\right) = x^{2} + \frac{1}{x^{2}} \]
holds for every \(x \in \mathbb{R}^{+}\)?
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Serbian National Competition (Drzavno takmicenje) 2009, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source