MathDB

3

Part of 1984 Iran MO (2nd round)

Problems(1)

The function has derivative - [Iran Second Round 1984]

Source:

12/30/2010
Let f:R→Rf : \mathbb R \to \mathbb R be a function such that f(x+y)=f(x)⋅f(y)∀x,y∈Rf(x+y)=f(x) \cdot f(y) \qquad \forall x,y \in \mathbb R Suppose that f(0)≠0f(0) \neq 0 and f(0)f(0) exists and it is finite (f(0)≠∞)(f(0) \neq \infty). Prove that ff has derivative in each point x∈R.x \in \mathbb R.
functioncalculusderivativegeometrygeometric transformationalgebra unsolvedalgebra