Find all functions \(f (x)\) such that \(f (2x + 1) = 4x^2 + 14x + 7\).
Construct a function defined at all points on a real line which is continuous at exactly one point.
Prove that the function \(\cos \sqrt {x}\) is not periodic.
Prove that for a monotonically increasing function \(f (x)\) the equations \(x = f (f (x))\) and \(x = f (x)\) are equivalent.
The numerical function \(f\) is such that for any \(x\) and \(y\) the equality \(f (x + y) = f (x) + f (y) + 80xy\) holds. Find \(f(1)\) if \(f(0.25) = 2\).