Let
be a continuous function ≠ 0 {\displaystyle {}\neq 0} , with the property that
for all x , y ∈ R {\displaystyle {}x,y\in \mathbb {R} } . Prove that f {\displaystyle {}f} is an exponential function, i.e. there exists a b > 0 {\displaystyle {}b>0} such that f ( x ) = b x {\displaystyle {}f(x)=b^{x}} .