Real function/Exponential equation/Continuous/Exponential function/Exercise

Let

$f:ℝ⟶ℝ$

be a continuous function $\ne 0$, with the property that

$f(x+y)=f(x)\cdot f(y)$

for all $x,y\in ℝ$. Prove that $f$ is an exponential function, i.e. there exists a $b>0$ such that $f(x)=b^x$.

Create a solution