Problem #PRU-116433

Problems Calculus Functions of one variable. Continuity Functions. Continuity (other) Algebra Sequences Progressions Geometric progression

14–16 3.0

Problem

The function $f (x)$ is defined on the positive real $x$ and takes only positive values. It is known that $f (1) + f (2) = 10$ and $f (a + b) = f (a) + f (b) + 2 \sqrt{f (a) f (b)}$ for any $a$ and $b$ . Find $f (2^{2011})$ .

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