Additive and multiplicative function.

There is a standard trick to this. The sketch of the argument is

  • $f$ maps squares to squares
  • $f$ maps nonnegative numbers to nonnegative numbers (since they are precisely the squares)
  • $f$ is monotone increasing, since $x \leq y$ iff $y-x$ is nonnegative

Tags:

Calculus

Functions

Real Analysis

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